A353524 - OEIS

%I #7 Apr 30 2022 22:51:42

%S 1,1,1,2,1,1,1,2,2,4,1,2,1,1,1,2,3,3,1,1,1,2,1,1,1,1,1,2,1,1,1,2,2,4,

%T 1,2,2,4,4,8,2,4,1,2,2,4,3,6,1,2,2,4,1,2,1,2,2,4,1,2,1,1,1,2,3,3,1,2,

%U 2,4,3,6,3,3,3,6,9,9,1,1,1,2,3,3,1,1,1,2,3,3,1,1,1,2,1,1,1,2,2,4,1,2,1,1,1,2

%N A003557 applied to the prime shadow of primorial base exp-function: a(n) = A003557(A181819(A276086(n))).

%H Antti Karttunen, <a href="/A353524/b353524.txt">Table of n, a(n) for n = 0..11550</a>

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

%F a(n) = A351944(A276086(n)) = A003557(A328835(n)) = A003557(A181819(A276086(n))).

%F For n > 0, a(n) = A353576(n) / A353577(n).

%o (PARI)

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A353524(n) = A003557(A181819(A276086(n)));

%Y Cf. A003557, A181819, A276086, A328835, A351944, A353576, A353577.

%K nonn,base

%O 0,4

%A _Antti Karttunen_, Apr 30 2022