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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000

Index entries for sequences related to factorial numbers.

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

Cf. A000142, A100685, A101976, A101977.

Sequence in context: A053145 A192589 A266448 * A076273 A024455 A038045

Adjacent sequences:  A101975 A101976 A101977 * A101979 A101980 A101981

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Dec 22 2004

STATUS

approved

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Last modified August 7 16:00 EDT 2022. Contains 355994 sequences. (Running on oeis4.)