This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038024 #18 Feb 16 2025 08:32:37 %S A038024 1,1,2,4,8,14,30,36,64,110,270,252,792,1008,1440,1344,5376,3936,14688, %T A038024 11664,19760,35200,96000,50880,97152,192192,145152,239904,917280, %U A038024 498240,2332800,864000,2334720,4300800,4257792,3172608 %N A038024 Number of k's such that A002034(k) = n. %H A038024 Paul Erdős, S. W. Graham, Alexsandr Ivić, and Carl Pomerance, <a href="http://people.cst.cmich.edu/graha1sw/Pub/Papers/divfactorial.pdf">On the number of divisors of n!</a>, 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. 337-355. %H A038024 J. Sondow and E. W. Weisstein, <a href="https://mathworld.wolfram.com/SmarandacheFunction.html">MathWorld: Smarandache Function</a> %F A038024 a(n) = A027423(n)-A027423(n-1) = A000005(A000142(n))-A000005(A000142(n-1)) i.e., number of divisors of n! which are not divisors of (n-1)! [for n>1]. - _Henry Bottomley_, Oct 22 2001 %F A038024 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 %t A038024 a[n_] := DivisorSigma[0, n!] - DivisorSigma[0, (n-1)!]; a[1] = 1; %t A038024 Array[a, 36] (* _Jean-François Alcover_, Sep 17 2020 *) %o A038024 (PARI) a(n)=numdiv(n!)-numdiv((n-1)!) \\ _Charles R Greathouse IV_, Jul 21 2015 %Y A038024 Cf. A046021. %K A038024 nonn %O A038024 1,3 %A A038024 _Christian G. Bower_