|
%I #13 Jun 29 2023 13:15:16
%S 1,1,1,2,2,3,3,6,2,5,5,10,10,70,210,210,210,35,35,14,14,154,154,462,
%T 2310,30030,10010,715,715,4290,4290,4290,4290,36465,7293,4862,4862,
%U 92378,277134,277134,277134,1939938,1939938,88179,146965,6760390,6760390,20281170
%N Products of primes the squares of which are Fermi-Dirac divisors of n!
%C Or equivalently, products of primes the squares of which are infinitary divisors of n!.
%H Rémy Sigrist, <a href="/A240505/b240505.txt">Table of n, a(n) for n = 1..5000</a>
%H Rémy Sigrist, <a href="/A240505/a240505.gp.txt">PARI program for A240505</a>
%o (PARI) isidiv(d, f) = {if (d==1, return (1)); for (k=1, #f~, bne = binary(f[k,2]); bde = binary(valuation(d, f[k,1])); if (#bde < #bne, bde = concat(vector(#bne-#bde), bde)); for (j=1, #bne, if (! bne[j] && bde[j], return (0)););); return (1);}
%o a(n) = {f = factor(n!); for (k=1, #f~, if ((f[k,2] > 1) && isidiv(f[k,1]^2, f), f[k,2]=1, f[k,2]=0);); factorback(f);} \\ _Michel Marcus_, Feb 15 2016
%Y Cf. A050376, A055204, A240502, A240504.
%K nonn
%O 1,4
%A _Vladimir Shevelev_, Apr 06 2014
%E a(23)-a(32) from _Michel Marcus_, Feb 15 2016
%E a(1) = 1 and more terms from _Rémy Sigrist_, Feb 13 2019
|
