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Numbers k that divide the sum of the first k nonprimes.
3

%I #11 Jan 04 2024 17:45:07

%S 1,8,32,44,577,5066,5669,8615,39787,59689,109752,146328,15451380,

%T 22173220,28558717,332573533,1837410366,3289933379,19053646133,

%U 370648112641

%N Numbers k that divide the sum of the first k nonprimes.

%C A variant of A045345 and A053781.

%C a(21) > 10^12. - _Donovan Johnson_, May 20 2010

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

%p 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

%t 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 *)

%Y 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).

%K nonn,more

%O 1,2

%A _J. M. Bergot_, May 14 2007

%E Edited and a(5) to a(18) added by _Klaus Brockhaus_, May 17 2007

%E a(19) from _Donovan Johnson_, Sep 19 2009

%E a(20) from _Donovan Johnson_, May 20 2010