A339894 - OEIS

%I #7 Dec 21 2020 23:03:54

%S 0,1,2,1,3,2,4,2,3,3,5,3,6,4,4,2,7,3,8,4,5,5,9,3,4,6,4,5,10,4,11,3,6,

%T 7,5,4,12,8,7,4,13,5,14,6,5,9,15,4,6,5,8,7,16,5,6,5,9,10,17,5,18,11,6,

%U 3,7,6,19,8,10,6,20,5,21,12,6,9,7,7,22,5,5,13,23,6,8,14,11,6,24,6,8,10,12,15,9,4,25

%N a(n) = A000523(A122111(n)).

%H Antti Karttunen, <a href="/A339894/b339894.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A339894/a339894.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A000523(A122111(n)).

%o (PARI)

%o A000523(n) = if( n<1, 0, #binary(n) - 1);

%o A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));

%o A339894(n) = A000523(A122111(n));

%Y Cf. A000523, A122111, A339895, A339896.

%K nonn

%O 1,3

%A _Antti Karttunen_, Dec 21 2020