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

1,4

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

Prog

(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

Crossrefs

Cf. A050376, A055204, A240502, A240504.

Sequence in context: A103403 A052473 A165122 * A051715 A143269 A036817

Adjacent sequences: A240502 A240503 A240504 * A240506 A240507 A240508

Keyword

nonn

Author

Vladimir Shevelev, Apr 06 2014

Extensions

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

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

Status

approved