A337335 - OEIS

%I #9 Aug 24 2020 22:29:20

%S 1,1,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,29,1,1,1,1,1,1,1,5,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,19,1,13,1,1,1,13,1,1,1

%N a(n) = gcd(A048673(n), 1+A003973(n)).

%H Antti Karttunen, <a href="/A337335/b337335.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>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = gcd(A048673(n), 1+A003973(n)) = (n) = gcd((1+A003961(n))/2, 1+sigma(A003961(n))).

%F For all n>= 1, a(A000290(n)) = A337337(n).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A337335(n) = { my(s=A003961(n)); gcd((1+s)/2, 1+sigma(s)); };

%Y Cf. A003961, A003973, A048673, A337337, A337342 (positions where equal to A048673).

%Y Cf. also A336850.

%K nonn

%O 1,10

%A _Antti Karttunen_, Aug 24 2020