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A173663 Numbers k that divide the k-th partial sum of all semiprimes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 28 10:56 EDT 2021. Contains 348327 sequences. (Running on oeis4.)