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A118219 Smallest number k>1 such that Sum_{i=1..k} Prime[i]^n divides Product_{i=1..k} Prime[i]^n. 0
3, 30, 17, 248, 515, 49682 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

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

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 *)

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.

Sequence in context: A108739 A072973 A154054 * A186681 A295430 A344430

Adjacent sequences:  A118216 A118217 A118218 * A118220 A118221 A118222

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk, Feb 24 2007

EXTENSIONS

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

STATUS

approved

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Last modified September 26 16:14 EDT 2021. Contains 347669 sequences. (Running on oeis4.)