cp's OEIS Frontend

A336856 Prime-shifted analog of gcd(d(n), sigma(n)): a(n) = gcd(A000005(n), A003973(n)).

%I A336856 #17 Aug 17 2020 20:52:02
%S A336856 1,2,2,1,2,4,2,4,1,4,2,6,2,4,4,1,2,2,2,2,4,4,2,8,3,4,4,6,2,8,2,2,4,4,
%T A336856 4,1,2,4,4,8,2,8,2,2,2,4,2,2,1,6,4,6,2,8,4,8,4,4,2,12,2,4,6,1,4,8,2,2,
%U A336856 4,8,2,4,2,4,6,6,4,8,2,2,1,4,2,12,4,4,4,8,2,4,4,6,4,4,4,12,2,2,2,3,2,8,2,8,8
%N A336856 Prime-shifted analog of gcd(d(n), sigma(n)): a(n) = gcd(A000005(n), A003973(n)).
%H A336856 Antti Karttunen, <a href="/A336856/b336856.txt">Table of n, a(n) for n = 1..65537</a>
%H A336856 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A336856 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A336856 a(n) = A009205(A003961(n)).
%F A336856 a(n) = gcd(A000005(n), A003973(n)) = gcd(A000005(n), A336841(n)).
%F A336856 a(n) = gcd(A000005(n), 2*A336840(n)).
%F A336856 a(n) = A003973(n) / A336838(n) = A000005(n) / A336839(n).
%F A336856 For n > 1, a(n) = A336841(n) / A336837(n).
%F A336856 For all primes p, and n >= 0, a(p^((2^n)-1)) = 2^n.
%o A336856 (PARI)
%o A336856 A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
%o A336856 A336856(n) = gcd(numdiv(n), A003973(n));
%Y A336856 Cf. A000005, A003961, A003973, A009205, A336837, A336838, A336839, A336840, A336841.
%K A336856 nonn
%O A336856 1,2
%A A336856 _Antti Karttunen_, Aug 12 2020