A128166 Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^2 = 1 + A024450(k).

1, 2, 3, 4, 6, 9, 12, 13, 26, 28, 45, 66, 174, 308, 350, 366, 417, 783, 804, 3774, 5714, 7998, 17628, 17940, 63447, 67620, 83028, 137868, 216717, 297486, 425708, 659316, 674166, 883500, 1203786, 3605052, 6778607, 9516098, 19964862, 25338586, 27771732, 70980884, 91871891, 208234138, 231967260, 238066596, 289829748, 784027092, 1078515812, 33256634230

Offset: 1

Author

Alexander Adamchuk, Feb 22 2007, Feb 23 2007

Keywords

• hard
• nonn

Comments

a(51) > 5.3*10^10. - Robert Price, Dec 16 2013

a(67) > 7*10^13. - Bruce Garner, May 05 2021

Links

• Bruce Garner, Table of n, a(n) for n = 1..66
• OEIS Wiki, Sums of powers of primes divisibility sequences

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

Mathematica

s = 1; Do[s = s + Prime[n]^2; If[ Mod[s, n] == 0, Print[n]], {n, 700000}]
(* or *)
Select[Range[10^4], IntegerQ[(1 + Plus@@(Prime[Range[#]]^2))/#] &] (* Alonso del Arte, Jan 20 2011 *)

Extensions

More terms from Sean A. Irvine, Jan 20 2011

a(45)-a(50) from Robert Price, Dec 16 2013