A354872 - OEIS

%I #8 Jun 12 2022 22:53:19

%S 1,1,1,1,3,1,1,1,4,1,1,1,1,5,1,1,5,1,5,3,2,1,5,1,7,1,3,1,6,1,1,7,8,7,

%T 1,1,9,2,1,1,7,1,7,7,10,1,3,1,7,9,2,1,7,4,7,5,11,1,7,1,12,1,1,3,8,1,3,

%U 11,8,1,7,1,13,2,5,9,9,1,7,1,14,1,2,5,15,3,2,1,8,5,11,13,16,11,7,1,9,3,2,1,10

%N a(n) = A056239(n) / gcd(A056239(n), A258851(n)).

%C Numerator of fraction A056239(n) / A258851(n).

%H Antti Karttunen, <a href="/A354872/b354872.txt">Table of n, a(n) for n = 2..65537</a>

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

%F a(n) = A056239(n) / A354871(n) = A056239(n) / gcd(A056239(n), A258851(n)).

%o (PARI)

%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }

%o A258851(n) = (n*sum(i=1, #n=factor(n)~, n[2, i]*primepi(n[1, i])/n[1, i])); \\ From A258851

%o A354872(n) = { my(u=A056239(n)); (u/gcd(u, A258851(n))); };

%o \\ Or:

%o A354872(n) = numerator(A056239(n)/A258851(n));

%Y Cf. A056239, A258851, A278510, A354871, A354873 (denominators).

%K nonn,frac

%O 2,5

%A _Antti Karttunen_, Jun 11 2022