A118219 Smallest number k>1 such that Sum_{i=1..k} Prime[i]^n divides Product_{i=1..k} Prime[i]^n.

3, 30, 17, 248, 515, 49682

Offset: 1

Author

Alexander Adamchuk, Feb 24 2007

Keywords

• hard
• more
• nonn

Comments

a(7)>991430. - Robert G. Wilson v, Mar 02 2007

Examples

			a(1) = 3 because 2 + 3 + 5 = 10 divides 2*3*5 = 30 but 2 + 3 = 5 does not divide 2*3 = 6.
		

Crossrefs

Cf. A051838 = Sum of first n primes divides product of first n primes. Cf. A125314 = Smallest number k>1 such that Sum_{i=1..k} i^n divides Product_{i=1..k} i^n. Cf. A007504, A002110, A024450, A098999, A122102, A122103.

Programs

Mathematica

f[n_] := Block[{k = 2, p = 2, s = 2^n}, While[p = p*Prime@ k; s = s + Prime@ k^n; PowerMod[p, n, s] != 0, k++ ]; k]; Do[ Print@ f@n, {n, 10}] (* Robert G. Wilson v *)

Extensions

a(6) from Robert G. Wilson v, Mar 02 2007