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

Author

Robert Price, Dec 12 2013

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

• OEIS Wiki, Sums of powers of primes divisibility sequences

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.

Programs

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 *)

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

Formula

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

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