A173663 Numbers k that divide the k-th partial sum of all semiprimes.

1, 2, 9, 19, 29, 44, 632, 11829, 19262, 25286, 26606, 29824, 247273, 310556, 491240, 1419166, 1601984, 9509238, 113333959, 220531559, 1034662494, 8323088842, 13102043650, 14053673678, 23505911647

Offset

1,2

Comments

a(26) > 3*10^10. - Donovan Johnson, Nov 26 2010

Links

Table of n, a(n) for n=1..25.

Formula

{k: k | Sum_{i=1..k} A001358(i)}.

Example

a(1) = 1 because 1 divides the first semiprime 4, trivially also the first partial sum of all semiprimes.
a(2) = 2 because A062198(2) = A001358(1) + A001358(2) = 4 + 6 = 10 is divisible by 2.
a(3) = 9 because A062198(9) = 126 = 2 * 3^2 * 7 is divisible by 9.
a(4) = 19 because A062198(19) = 532 = 2^2 * 7 * 19 is divisible by 19.
a(5) = 29 because A062198(29) = 1247 = 29 * 43 is divisible by 29.
a(6) = 44 because A062198(44) = 2904 = 44 * 66.

Mathematica

SemiprimeQ[n_Integer] := If[Abs[n]<2, False, (2==Plus@@Transpose[FactorInteger[Abs[n]]][[2]])]; nn=10^6; sm=0; cnt=0; Reap[Do[If[SemiprimeQ[n], cnt++; sm=sm+n; If[Divisible[sm, cnt], Sow[cnt]]], {n, nn}]][[2, 1]]

Prog

(PARI) s=0; p=0; for(n=1, 1e9, until(bigomega(p++)==2, ); (s+=p)%n | print1(n", ")) \\ M. F. Hasler, Nov 24 2010

Crossrefs

Cf. A001358, A007506.

Sequence in context: A075340 A031316 A335051 * A294546 A135207 A274853

Adjacent sequences: A173660 A173661 A173662 * A173664 A173665 A173666

Keyword

nonn,more

Author

Jonathan Vos Post, Nov 24 2010

Extensions

Extended by T. D. Noe, Nov 24 2010

a(1)-a(17) double-checked and a(18) from M. F. Hasler, Nov 25 2010

a(19) from Ray Chandler, Nov 25 2010

a(20)-a(25) from Donovan Johnson, Nov 26 2010

Status

approved