A354871 - OEIS

%I #9 Jun 12 2022 22:53:16

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

%T 1,1,6,12,1,4,6,13,1,14,1,1,1,15,2,8,1,1,4,16,1,2,1,2,1,17,1,18,1,8,6,

%U 3,1,19,3,1,1,20,1,21,1,4,2,1,1,22,1,8,1,23,4,2,1,4,4,24,1,2,1,1,1,1,1,25,1,3,4

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

%H Antti Karttunen, <a href="/A354871/b354871.txt">Table of n, a(n) 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) = gcd(A056239(n), A258851(n)).

%F a(n) = gcd(A056239(n), A278510(n)) = gcd(A258851(n), A278510(n)).

%F For n > 1, a(n) = A056239(n) / A354872(n) = A258851(n) / A354873(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 A354871(n) = gcd(A056239(n), A258851(n));

%Y Cf. A056239, A258851, A278510, A354872, A354873.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 11 2022