A217601 Integer averages of squares of first primes.

4, 1314, 7128, 3081302, 4009568, 5312966, 16834447856, 2462344442400, 289274033242208, 46671783125431818542, 221000817555367050608, 618811172463743796896678, 13954866972387224169218132, 176536110349401666017009273532, 996528450408723697487070591774

Offset: 1

Author

Robert Price, Mar 19 2013

Keywords

• nonn

Examples

			a(2) = 1314 is the average of squares of first 19 primes (24966/19=1314).
		

Links

• Paul W. Dyson, Table of n, a(n) for n = 1..16
• 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, A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

PARI

n=s=0; forprime(p=2,1e8, s+=p^2; if(s%n++==0, print1(s/n", "))) \\ Charles R Greathouse IV, Apr 22 2015

Formula

a(n) = A217600(n)/A111441(n).

Extensions

a(13) from Karl-Heinz Hofmann, Dec 08 2020

a(14) from Karl-Heinz Hofmann, Dec 26 2020

a(15) from Karl-Heinz Hofmann, Dec 27 2020