A375636 The number of infinitary divisors of n! that are factorials.
1, 2, 3, 4, 5, 2, 3, 5, 3, 2, 3, 4, 5, 5, 3, 5, 6, 2, 3, 2, 3, 5, 6, 2, 3, 3, 5, 4, 5, 2, 3, 6, 12, 2, 2, 2, 3, 5, 3, 4, 5, 7, 8, 4, 4, 2, 3, 2, 2, 3, 6, 4, 5, 2, 3, 5, 7, 4, 5, 4, 5, 5, 3, 4, 12, 2, 3, 2, 2, 3, 4, 2, 3, 3, 6, 4, 4, 2, 3, 4, 2, 3, 4, 4, 4, 2, 2
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
expQ[e1_, e2_] := Module[{m = Length[e2], ans = 1}, Do[If[BitAnd[e1[[i]], e2[[i]]] < e2[[i]], ans = 0; Break[]], {i, 1, m}]; ans]; e[n_] := e[n] = FactorInteger[n!][[;; , 2]]; a[n_] := 1 + Sum[expQ[e[n], e[m]], {m, 2, n}]; Array[a, 100] -
PARI
isexp(e1, e2) = {my(m = #e2, ans = 1); for(i=1,m,if(bitand(e1[i], e2[i]) < e2[i], ans = 0; break)); ans;} e(n) = factor(n!)[,2]; a(n) = 1 + sum(m = 2, n, isexp(e(n), e(m)));