A377723 Contribution to the OEIS

 A377723

Numbers whose number of prime factors (counted with repetition) is greater than or equal to its smallest prime factor.

0

4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116

(list; graph; refs; listen; history; edit; text; internal format)

OFFSET

1,1

COMMENTS

Numbers k such that A001222(k) >= A020639(k).

Complement of A091377.

A091371(a(n)) < 1: A001222(a(n)) => A020639(a(n)).

LINKS

James C. McMahon, Table of n, a(n) for n = 1..10000

EXAMPLE

4 is a term because bigomega(4) = spf(4) = 2.

12 is a term because bigomega(12) = 3 > spf(12) = 2.

3 is not a term because bigomega(3) = 1 < spf(3) = 3.

MATHEMATICA

Select[Range[116], PrimeOmega[#]>=FactorInteger[#][[1, 1]]&]

CROSSREFS

Cf. A001222, A020639, A091371, A091375, A091376, A091377.

Sequence in context: A330948 A324705 A032583 * A175074 A063127 A272651

Adjacent sequences: A377720 A377721 A377722 * A377724 A377725 A377726

KEYWORD

nonn,new

AUTHOR

James C. McMahon, Dec 28 2024

STATUS

approved

The Newest Boring Number: 20990

In a prior post, 20067 was described as a "boring" number. It was considered boring because it was the lowest number not occurring in the On-Line Encyclopedia of Integer Sequences (OEIS). 

However, this month, a new OEIS sequence was published, including 20667 as a term. The sequence is: A379570 - OEIS. 20667 is the fifth sequence term defined by "Number of n-digit numbers that have exactly 8 divisors."

So now, the lowest number not occurring in the OEIS is: 20990.

Update 1/2/2025. Just after 20067 was replaced by a new most boring number, a sequence that included the prime number 45247 was submitted, so it lost its designation as the most boring prime number. Now, the lowest prime number not occurring in the OEIS is 48973 (the 5033rd prime).

The new sequence including 45247 is: A379615 Numerators of the partial sums of the reciprocals of the sum of bi-unitary divisors function (A188999).

A378384 Contribution to the OEIS

 A378384

Digital root of the sum of the previous 3 terms; a(0) = a(1) = a(2) = 1.

0

1, 1, 1, 3, 5, 9, 8, 4, 3, 6, 4, 4, 5, 4, 4, 4, 3, 2, 9, 5, 7, 3, 6, 7, 7, 2, 7, 7, 7, 3, 8, 9, 2, 1, 3, 6, 1, 1, 8, 1, 1, 1, 3, 5, 9, 8, 4, 3, 6, 4, 4, 5, 4, 4, 4, 3, 2, 9, 5, 7, 3, 6, 7, 7, 2, 7, 7, 7, 3, 8, 9, 2, 1, 3, 6, 1, 1, 8, 1, 1, 1, 3, 5, 9, 8, 4, 3, 6

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

This differs from A112661 which is sum of digits of sum of previous 3 terms.

Digital root of A000213 (tribonacci numbers beginning {1,1,1}).

This has a period of 39 beginning with the first term.

Decimal expansion of 12373315960504936995263080863765792902/111111111111111111111111111111111111111 = 0.[111359843644544432957367727773892136118] (periodic).

LINKS

Table of n, a(n) for n=0..87.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

FORMULA

a(n) = A010888(A000213(n)).

MATHEMATICA

Nest[Append[#, ResourceFunction["AdditiveDigitalRoot"][Total[Take[#, -3]]]]&, {1, 1, 1}, 85]

CROSSREFS

Cf. A000213, A010888, A112661.

Sequence in context: A221967 A079428 A094548 * A112661 A230725 A254689

Adjacent sequences: A378381 A378382 A378383 * A378386 A378388 A378389

KEYWORD

nonn,base,easy,new

AUTHOR

James C. McMahon, Nov 24 2024

STATUS

approved