A351232 - OEIS

%I #12 Feb 05 2022 17:06:14

%S 3,6,2,18,1,10,1,5,6,90,1,50,8,18,7,450,5,250,15,75,86,2250,14,125,

%T 125,138,175,11250,0,14,0,3,3,10,0,70,5,13,4,630,4,350,10,26,63,3150,

%U 7,125,58,262,140,15750,54,546,142,1193,1270,78750,0,98,4,5,2,49,4,490,10,56,37,4410,7,2450,94,133,137,1225

%N a(n) = floor(A276086(n) / A003415(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%H Antti Karttunen, <a href="/A351232/b351232.txt">Table of n, a(n) for n = 2..11050</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = floor(A276086(n) / A003415(n)) = floor(A351231(n) / A351230(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 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A351232(n) = floor(A276086(n) / A003415(n));

%Y Cf. A003415, A276086, A351230, A351231.

%Y Cf. A351228 (conjectured to give the positions of zeros from its second term onward).

%K nonn,base,easy,look

%O 2,1

%A _Antti Karttunen_, Feb 05 2022