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%I #27 May 09 2020 15:28:03
%S 1,7,13,17,19,24,25,27,31,32,34,37,38,43,45,47,49,55,57,59,61,62,64,
%T 67,71,73,76,77,79,80,84,85,87,91,92,93,94,97,101,103,104,107,109,110,
%U 115,117,118,121,122,123,124,127,129,132,133,137,139,142,143,144,145,147
%N Numbers k such that Sum_{i=1..k} i^2 divides Product_{i=1..k} i^2.
%C Product_{i=1..k} i^2 = (k!)^2 and Sum_{i=1..k} i^2 = k*(k+1)*(2*k+1)/6. - J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010
%H J. Mulder, <a href="/A166602/b166602.txt">Table of n, a(n) for a(n) below 20000</a>
%e a(2) = A125314(2) = 7.
%p q:= k-> is(irem(k!^2, k*(k+1)*(2*k+1)/6)=0):
%p select(q, [$1..200])[]; # _Alois P. Heinz_, May 09 2020
%t Cases[Range[2, 5000], k_ /; Divisible[Factorial[k - 1]^2, 1/6 (-1 + k) k (-1 + 2 k)]] - 1 (* J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010 *)
%o (PARI) isok(k) = ((k!)^2 % (k*(k+1)*(2*k+1)/6)) == 0; \\ _Michel Marcus_, May 09 2020
%Y Cf. A000330, A001044, A125294, A125314, A060462, A166604, A166605, A166606, A166607, A166608, A166609, A166610, A334735.
%Y Cf. A067656. - _R. J. Mathar_, Oct 23 2009
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Oct 18 2009
%E Terms below 5000 by J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010
%E More terms copied from the b-file by _R. J. Mathar_, Feb 14 2010
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