A373083 Contribution to the OEIS

 

A373083 a(1) = 1; for n > 1, a(n) = a(n-1) + n if n is prime, else a(n) = a(n-1) + largest divisor of n < n. 0

1, 3, 6, 8, 13, 16, 23, 27, 30, 35, 46, 52, 65, 72, 77, 85, 102, 111, 130, 140, 147, 158, 181, 193, 198, 211, 220, 234, 263, 278, 309, 325, 336, 353, 360, 378, 415, 434, 447, 467, 508, 529, 572, 594, 609, 632, 679, 703, 710, 735, 752, 778, 831, 858, 869, 897 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 1,2 COMMENTS Differs from A219730 at a(12). LINKS James C. McMahon, Table of n, a(n) for n = 1..1000 FORMULA a(n) = a(n-1) + A117818(n) for n > 1. - Michael De Vlieger, Jun 23 2024 EXAMPLE From Michael De Vlieger, Jun 23 2024: (Start) Let lpf = A020639(n). a(2) = 3 since 2 is prime, therefore a(1) + 2 = 3. a(3) = 6 since 3 is prime, therefore a(2) + 3 = 6. a(4) = 8 since 4 is not prime, therefore a(3) + 4/lpf(4) = 6 + 2 = 8. a(5) = 13 since 5 is prime, therefore a(4) + 5 = 13. a(6) = 16 since 6 is not prime, hence a(5) + 6/lpf(6) = 13 + 3 = 16, etc. (End) MATHEMATICA a[1]=1; a[n_]:=If[PrimeQ[n], a[n-1]+n, a[n-1]+Divisors[n][[-2]]]; Table[a[n], {n, 56}] CROSSREFS Cf. A117818, A219730. Sequence in context: A046670 A131383 A219730 * A337484 A139001 A090961 Adjacent sequences: A373080 A373081 A373082 * A373084 A373085 A373086 KEYWORD nonn,easy,new AUTHOR James C. McMahon, Jun 17 2024 STATUS approved