A351950 Arithmetic derivative of the factorial base exp-function: a(n) = A003415(A276076(n)).

0, 1, 1, 5, 6, 21, 1, 7, 8, 31, 39, 123, 10, 45, 55, 185, 240, 705, 75, 275, 350, 1075, 1425, 3975, 1, 9, 10, 41, 51, 165, 12, 59, 71, 247, 318, 951, 95, 365, 460, 1445, 1905, 5385, 650, 2175, 2825, 8275, 11100, 30075, 14, 77, 91, 329, 420, 1281, 119, 483, 602, 1939, 2541, 7287, 840, 2905, 3745, 11165, 14910, 40845

Offset: 0

Author

Antti Karttunen, Apr 01 2022

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A003415, A276076, A351576, A351952.

Differs from a similarly defined A327860 for the first time at n=24.

Coincides with A351951 on n given by A059590.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276076(n) = { my(i=0,m=1,f=1,nextf); while((n>0),i=i+1; nextf = (i+1)*f; if((n%nextf),m*=(prime(i)^((n%nextf)/f));n-=(n%nextf));f=nextf); m; };
A351950(n) = A003415(A276076(n));

Formula

a(n) = A003415(A276076(n)).

a(n) = A327860(A351576(n)).