A129749 Numbers k that divide the sum of the first k nonprimes.

1, 8, 32, 44, 577, 5066, 5669, 8615, 39787, 59689, 109752, 146328, 15451380, 22173220, 28558717, 332573533, 1837410366, 3289933379, 19053646133, 370648112641

Offset

1,2

Comments

A variant of A045345 and A053781.

a(21) > 10^12. - Donovan Johnson, May 20 2010

Links

Table of n, a(n) for n=1..20.

Example

The sum of the first 44 nonprimes is 1452 = 33*44.

Maple

np:=proc(j) if isprime(j)=false then j else fi end: NP:=[seq(np(j), j=1..50000)]: a:=proc(n) if type(add(NP[j], j=1..n)/n, integer)=true then n else fi end: seq(a(n), n=1..nops(NP)); # Emeric Deutsch, May 16 2007

Mathematica

Module[{nn=150000, np}, np=Accumulate[Select[Range[nn], !PrimeQ[#]&]]; Select[Thread[ {np, Range[Length[np]]}], Mod[#[[1]], #[[2]]]==0&]][[;; , 2]] (* The program generates the first 11 terms of the sequence. To generate more, increase the nn constant. *) (* Harvey P. Dale, Jan 04 2024 *)

Crossrefs

Cf. A045345 (n divides sum of first n primes), A053781 (n divides sum of first n composites), A018252 (nonprimes), A051349 (sum of first n nonprimes).

Sequence in context: A371444 A127988 A371454 * A005879 A067519 A253295

Adjacent sequences: A129746 A129747 A129748 * A129750 A129751 A129752

Keyword

nonn,more

Author

J. M. Bergot, May 14 2007

Extensions

Edited and a(5) to a(18) added by Klaus Brockhaus, May 17 2007

a(19) from Donovan Johnson, Sep 19 2009

a(20) from Donovan Johnson, May 20 2010

Status

approved