A263546 Numbers k such that k divides the sum of the first k primes with even indices.

1, 2, 6, 12, 15, 28, 40, 92, 111, 113, 145, 223, 268, 420, 625, 2080, 2282, 2996, 3371, 19560, 38032, 54426, 1474778, 3763906, 5196340, 6435993, 7808592, 11487666, 16738298, 28145334, 53830258, 57281504, 77275294, 135770496, 164914949

Offset: 1

Author

Altug Alkan, Oct 20 2015

Keywords

• nonn

Comments

There are 15 values of a(n) < 1000 although A045345 has 4 values A045345(n) < 1000. How do these sequences compare asymptotically?

Examples

			1 is in the sequence because prime(2) = 3 is divisible by 1.
2 is in the sequence because prime(2) + prime(4) = 3 + 7 = 10 is divisible by 2.
		

Crossrefs

Cf. A031215, A045345, A077126, A263541.

Programs

Mathematica

Select[Range@ 10000, Divisible[Sum[Prime[2 i], {i, 1, #}], #] &] (* Michael De Vlieger, Oct 21 2015 *)

PARI

list(lim)=my(v=List(), k, s, t); forprime(p=2, ,if((t++) && t%2==0, s+=p; k++; if(s%k==0, listput(v, k)); if(k>=lim, return(Vec(v)))))