A233555 Prime(m), where m is such that (Sum_{i=1..m} prime(i)^17) / m is an integer.

2, 5724469, 10534369, 16784723, 33330911, 189781037, 8418091991, 58605633953, 109388266843, 448366797199, 1056238372873, 24603683667221, 86982253895059, 100316149840769, 164029709175817, 542295448805641, 685217940914237, 1701962315686097, 23064173255594491

Offset

1,1

Comments

a(18) > 1005368767096627. - Bruce Garner, Aug 30 2021

a(19) > 1701962315686097. - Bruce Garner, Jan 07 2022

Links

Table of n, a(n) for n=1..19.

OEIS Wiki, Sums of powers of primes divisibility sequences

Formula

a(n) = prime(A131277(n)).

Example

a(1) = 2, because 2 is the 1st prime and the sum of the first 1 primes^17 = 131072 when divided by 1 equals 131072 which is an integer.

Mathematica

t = {}; sm = 0; Do[sm = sm + Prime[n]^17; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

Prog

(PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^17); s==0 \\ Charles R Greathouse IV, Nov 30 2013
(PARI) S=n=0; forprime(p=1, , (S+=p^17)%n++||print1(p", ")) \\ M. F. Hasler, Dec 01 2013

Crossrefs

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

Cf. A000040, A007504, A045345, A171399, A128165, A233523, A050247, A050248.

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

Sequence in context: A273354 A352126 A157991 * A273729 A324440 A121390

Adjacent sequences: A233552 A233553 A233554 * A233556 A233557 A233558

Keyword

nonn

Author

Robert Price, Dec 12 2013

Extensions

a(12) from Bruce Garner, Mar 02 2021

a(13) from Bruce Garner, Mar 17 2021

a(14) from Bruce Garner, Mar 30 2021

a(15) from Bruce Garner, Apr 14 2021

a(16) from Bruce Garner, Jun 30 2021

a(17) from Bruce Garner, Aug 30 2021

a(18) from Bruce Garner, Jan 07 2022

a(19) from Paul W. Dyson, Sep 15 2023

Status

approved