A111452 Numbers k that divide the square of the sum of the first k primes.

1, 23, 25, 53, 297, 853, 10043, 11869, 117267, 222975, 241163, 339615, 3538161, 3600489, 25537223, 38576521, 95316169, 96643287, 225448535, 229337199, 2230825625, 2356693955, 2587096837, 2597720625, 2664167025, 11945834209, 30419894569, 43435512311, 50227870041

Offset

1,2

Comments

Each number in this sequence is odd. Every term of A045345 also occurs in this sequence.

Links

Giovanni Resta, Table of n, a(n) for n = 1..35

Example

(prime(1) + prime(2) + ... + prime(23))^2 = (2 + 3 + 5 + ... + 83)^2 = 23*33212.

Mathematica

s = 0; t = {}; Do[s = s + Prime[n]; If[ Mod[s^2, n] == 0, AppendTo[t, n]], {n, 10^8}]; t (* Robert G. Wilson v, Nov 15 2005 *)

Prog

(PARI) {my(k=0, s=0); forprime(p=2, prime(10^8), k++; s+=p; if(s^2%k==0, print1(k, ", ")))} \\ Andrew Howroyd, Jan 02 2020

Crossrefs

Cf. A045345.

Sequence in context: A172015 A112073 A050864 * A335180 A147627 A359510

Adjacent sequences: A111449 A111450 A111451 * A111453 A111454 A111455

Keyword

nonn

Author

Stefan Steinerberger, Nov 14 2005

Extensions

a(13)-a(18) from Robert G. Wilson v, Nov 15 2005

a(19)-a(25) from Andrew Howroyd, Jan 02 2020

a(26)-a(29) from Giovanni Resta, Jan 03 2020

Status

approved