login
A101978
Number of powers of factorials not exceeding n!.
3
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
1,2
COMMENTS
a(n) is the position of n! in A100685 (powers of factorials). a(n) < A101976(n) for n > 3 and a(n) < A101977(n) for n > 10.
EXAMPLE
a(4) = 7 because 7 powers of factorials do not exceed 4!, namely, 1, 2, 4, 6, 8, 16 and 24.
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Dec 22 2004
STATUS
approved