A351950 - OEIS

%I #10 Apr 02 2022 10:32:28

%S 0,1,1,5,6,21,1,7,8,31,39,123,10,45,55,185,240,705,75,275,350,1075,

%T 1425,3975,1,9,10,41,51,165,12,59,71,247,318,951,95,365,460,1445,1905,

%U 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

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

%H Antti Karttunen, <a href="/A351950/b351950.txt">Table of n, a(n) for n = 0..10080</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

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

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

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o 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; };

%o A351950(n) = A003415(A276076(n));

%Y Cf. A003415, A276076, A351576, A351952.

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

%Y Coincides with A351951 on n given by A059590.

%K nonn,base

%O 0,4

%A _Antti Karttunen_, Apr 01 2022