

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
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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 DuraKovács, 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 DuraKovács, Nov 25 2020


STATUS

approved



