

A038024


Number of k's such that A002034(k) = n.


3



1, 1, 2, 4, 8, 14, 30, 36, 64, 110, 270, 252, 792, 1008, 1440, 1344, 5376, 3936, 14688, 11664, 19760, 35200, 96000, 50880, 97152, 192192, 145152, 239904, 917280, 498240, 2332800, 864000, 2334720, 4300800, 4257792, 3172608
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


LINKS

Table of n, a(n) for n=1..36.
Paul Erdős, S. W. Graham, Alexsandr Ivić, and Carl Pomerance, On the number of divisors of n!, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, ed. by B. C. Berndt, H. G. Diamond, A. J. Hildebrand, Birkhauser 1996, pp. 337355.
J. Sondow and E. W. Weisstein, MathWorld: Smarandache Function


FORMULA

a(n) = A027423(n)A027423(n1) = A000005(A000142(n))A000005(A000142(n1)) i.e., number of divisors of n! which are not divisors of (n1)! [for n>1].  Henry Bottomley, Oct 22 2001
Erdős, Graham, Ivić, & Pomerance show that the average order of log a(n) is c log n/(log log n)^2 with c around 0.6289.  Charles R Greathouse IV, Jul 21 2015


MATHEMATICA

a[n_] := DivisorSigma[0, n!]  DivisorSigma[0, (n1)!]; a[1] = 1;
Array[a, 36] (* JeanFrançois Alcover, Sep 17 2020 *)


PROG

(PARI) a(n)=numdiv(n!)numdiv((n1)!) \\ Charles R Greathouse IV, Jul 21 2015


CROSSREFS

Cf. A046021.
Sequence in context: A244933 A118560 A187813 * A337500 A061297 A130711
Adjacent sequences: A038021 A038022 A038023 * A038025 A038026 A038027


KEYWORD

nonn


AUTHOR

Christian G. Bower


STATUS

approved



