A374671 Positive numbers k such that k! and (k+1)! have an equal number of infinitary divisors.

8, 19, 23, 44, 45, 57, 67, 76, 80, 83, 84, 85, 105, 107, 116, 120, 123, 140, 141, 146, 158, 161, 165, 174, 177, 187, 201, 208, 214, 225, 235, 239, 241, 243, 244, 246, 247, 263, 269, 272, 277, 284, 297, 309, 315, 321, 322, 325, 337, 339, 341, 342, 344, 360, 363

Offset

1,1

Comments

Positive numbers such that k! and (k+1)! have an equal number of Fermi-Dirac factors (A064547).

Positive numbers k such that A037445(k!) = A037445((k+1)!).

Positive numbers k such that A064547(k!) = A064547((k+1)!).

Positive numbers k such that A177329(k) = A177329(k+1).

Links

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

Example

8 is a term since A037445(8!) = A037445(9!) = 64.

Mathematica

s[n_] := s[n] = Module[{e = FactorInteger[n!][[;; , 2]]}, Sum[DigitCount[e[[k]], 2, 1], {k, 1, Length[e]}]]; Select[Range[2, 400], s[#] == s[# + 1] &]

Prog

(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); }

Crossrefs

Cf. A037445, A064547, A177329, A343819, A374672, A374673, A374674.

Sequence in context: A227881 A294581 A290185 * A274397 A178130 A227029

Adjacent sequences: A374668 A374669 A374670 * A374672 A374673 A374674

Keyword

nonn

Author

Amiram Eldar, Jul 16 2024

Status

approved