A374672 Numbers k such that k! has more infinitary divisors than (k+1)!.

5, 9, 17, 27, 33, 34, 35, 43, 48, 51, 53, 59, 65, 68, 69, 75, 77, 87, 91, 97, 98, 99, 103, 115, 119, 125, 129, 134, 135, 139, 147, 149, 151, 155, 163, 164, 171, 179, 183, 189, 194, 195, 197, 199, 203, 211, 215, 221, 227, 229, 230, 231, 237, 245, 249, 257, 259

Offset: 1

Author

Amiram Eldar, Jul 16 2024

Keywords

• nonn

Comments

Numbers k such that k! has more Fermi-Dirac factors (A064547) than (k+1)!.

Numbers k such that A037445(k!) > A037445((k+1)!).

Numbers k such that A064547(k!) > A064547((k+1)!).

Numbers k such that A177329(k) > A177329(k+1).

Examples

			5 is a term since A037445(5!) = 16 > A037445(6!) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037445, A064547, A177329, A343819, A374671, A374673, A374674.

Programs

Mathematica

s[n_] := s[n] = Module[{e = FactorInteger[n!][[;; , 2]]}, Sum[DigitCount[e[[k]], 2, 1], {k, 1, Length[e]}]]; Select[Range[2, 300], s[#] > s[# + 1] &]

PARI

s(n) = {my(e = factor(n!)[, 2]); sum(k=1, #e, hammingweight(e[k]));}
lista(kmax) = {my(s1 = s(1), s2); for(k = 2, kmax, s2 = s(k); if(s1 > s2, print1(k-1, ", ")); s1 = s2);}