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A111441 Numbers n such that the sum of the squares of the first n primes is divisible by n. 97
1, 19, 37, 455, 509, 575, 20597, 202717, 1864637, 542474231, 1139733677, 51283502951, 230026580777 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(13) > 2*10^11 if it exists. - Robert Price, Mar 19 2013

a(14) > 4*10^11 if it exists. - Balázs Dura-Kovács, Nov 25 2020

LINKS

Table of n, a(n) for n=1..13.

OEIS Wiki, Sums of powers of primes divisibility sequences.

EXAMPLE

The sum of the squares of the first 19 primes 2^2 + 3^2 + 5^2 + ... + 67^2 = 19*1314, thus 19 is in an element of the sequence.

MATHEMATICA

s = 0; t = {}; Do[s = s + Prime[n]^2; If[ Mod[s, n] == 0, AppendTo[t, n]], {n, 10^6}]; t (* Robert G. Wilson v, Nov 15 2005 *)

PROG

(MuPAD) a := 0; for n from 1 to 100000 do a := a + ithprime(n)^2; if a/n = trunc(a/n) then print(n); end_if; end_for;

(PARI) for(n=1, 2*10^11, m=n; s=0; while(m>0, s=s+prime(m)^2; m--); if(s%n==0, print1(n, ", "))) \\ Felix Fröhlich, Jul 07 2014

(PARI) isok(n) = norml2(primes(n)) % n == 0; \\ Michel Marcus, Nov 25 2020

CROSSREFS

Cf. A024450, A045345.

Sequence in context: A136063 A242979 A244931 * A144594 A287310 A123028

Adjacent sequences:  A111438 A111439 A111440 * A111442 A111443 A111444

KEYWORD

nonn,hard,more,changed

AUTHOR

Stefan Steinerberger, Nov 14 2005

EXTENSIONS

a(8)-a(9) from Robert G. Wilson v, Nov 15 2005

a(10)-a(11) from Ryan Propper, Mar 27 2007

a(12) from Robert Price, Mar 19 2013

a(13) from Balázs Dura-Kovács, Nov 25 2020

STATUS

approved

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Last modified November 29 18:07 EST 2020. Contains 338769 sequences. (Running on oeis4.)