A240505 Products of primes the squares of which are Fermi-Dirac divisors of n!

1, 1, 1, 2, 2, 3, 3, 6, 2, 5, 5, 10, 10, 70, 210, 210, 210, 35, 35, 14, 14, 154, 154, 462, 2310, 30030, 10010, 715, 715, 4290, 4290, 4290, 4290, 36465, 7293, 4862, 4862, 92378, 277134, 277134, 277134, 1939938, 1939938, 88179, 146965, 6760390, 6760390, 20281170

Offset: 1

Author

Vladimir Shevelev, Apr 06 2014

Keywords

• nonn

Comments

Or equivalently, products of primes the squares of which are infinitary divisors of n!.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..5000
• Rémy Sigrist, PARI program for A240505

Crossrefs

Cf. A050376, A055204, A240502, A240504.

Programs

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);}
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

Extensions

a(23)-a(32) from Michel Marcus, Feb 15 2016

a(1) = 1 and more terms from Rémy Sigrist, Feb 13 2019