A134129 Prime partial sums A007504(k+1) such that A007504(k+1)/k is integer.

5, 10, 28, 77, 160, 5350, 43940, 331608, 1464099, 111509916, 269629588, 316586861, 734973855, 6186337680, 10731699088, 22692172980, 148089006456, 474639489984, 6777589645423, 30458742769120, 215730372141680, 761593852850347, 5875984874989879, 10893969051902225

Offset

1,1

Comments

See A134125 and cross-references.

Links

Amiram Eldar, Table of n, a(n) for n = 1..32

Formula

a(n) = A007504(A134126(n+1)) .

Example

A007504(2)/1 = 5/1 = 5 is integer, so 5 is added to the sequence.
A007504(3)/2 = 10/2 = 5 is integer, so 10 is added to the sequence.
A007504(4)/3 = 17/3 is not integer, so 17 is not added to the sequence.

Prog

(UBASIC) 10 'primes using counters 20 N=3:C=1:R=5:print 2; 3, 5 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then N=N+2:goto 30 60 A=A+2:O=A 70 if A<=sqrt(N) then 40 80 C=C+1 90 R=R+N:T=R/C:U=R-N 100 if T=int(T) then print C; U; N; R; T:stop 110 N=N+2:goto 30
(PARI) lista(pmax) = {my(k = 0, s = 2); forprime(p = 3, pmax, k++; s += p; if(!(s % k), print1(s, ", "))); } \\ Amiram Eldar, Apr 30 2024

Crossrefs

Cf. A007504, A134125, A134126 A134127, A134128.

Sequence in context: A277825 A054298 A022094 * A240515 A105862 A338662

Adjacent sequences: A134126 A134127 A134128 * A134130 A134131 A134132

Keyword

nonn

Author

Enoch Haga, Oct 09 2007

Extensions

Edited by R. J. Mathar, May 15 2009

a(21)-a(24) from Amiram Eldar, Apr 30 2024

Status

approved