A101978 Number of powers of factorials not exceeding n!.
1, 2, 4, 7, 11, 17, 22, 29, 36, 43, 51, 60, 68, 76, 86, 96, 105, 116, 125, 136, 149, 159, 170, 183, 193, 206, 219, 230, 241, 254, 268, 281, 293, 306, 322, 335, 347, 362, 377, 390, 403, 417, 433, 447, 464, 475, 493, 508, 521, 537, 551, 568, 585, 598, 614, 632
Offset: 1
Keywords
Examples
a(4) = 7 because 7 powers of factorials do not exceed 4!, namely, 1, 2, 4, 6, 8, 16 and 24.
Links
Programs
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Mathematica
p[n_] := If[n>1, Union[Flatten[With[{ln=Log[n! ]}, Table[With[{f=m!}, Table[f^j, {j, 0, Floor[ln/Log[f]]}]], {m, 2, n}]]]], {1}]; Table[Length[p[n]], {n, 100}]
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