cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A334663 a(n) = Sum_{d|n} gcd(sigma(d), pod(d)), where pod(k) is the product of the divisors of k (A007955).

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%I A334663 #19 Sep 08 2022 08:46:25
%S A334663 1,2,2,3,2,15,2,4,3,5,2,20,2,7,6,5,2,19,2,8,4,7,2,33,3,5,4,64,2,93,2,
%T A334663 6,6,5,4,25,2,7,4,19,2,69,2,12,10,7,2,38,3,7,12,8,2,44,4,73,4,5,2,124,
%U A334663 2,7,6,7,4,167,2,8,6,27,2,41,2,5,8,12,4,43,2
%N A334663 a(n) = Sum_{d|n} gcd(sigma(d), pod(d)), where pod(k) is the product of the divisors of k (A007955).
%C A334663 Inverse Möbius transform of A306682. - _Antti Karttunen_, May 09 2020
%H A334663 Antti Karttunen, <a href="/A334663/b334663.txt">Table of n, a(n) for n = 1..16384</a>
%H A334663 Antti Karttunen, <a href="/A334663/a334663.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A334663 a(p) = 2 for p = primes (A000040).
%e A334663 a(6) = gcd(sigma(1), pod(1)) + gcd(sigma(2), pod(2)) + gcd(sigma(3), pod(3)) + gcd(sigma(6), pod(6)) = gcd(1, 1) + gcd(3, 2) + gcd(4, 3) + gcd(12, 36) = 1 + 1 + 1 + 12 = 15.
%o A334663 (Magma) [&+[GCD(&+Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]]
%o A334663 (PARI) a(n) = sumdiv(n, d, gcd(sigma(d), vecprod(divisors(d)))); \\ _Michel Marcus_, May 08 2020
%Y A334663 Cf. A334579 (Sum_{d|n} gcd(tau(d), sigma(d))), A334662 (Sum_{d|n} gcd(tau(d), pod(d))).
%Y A334663 Cf. A000203 (sigma(n)), A007955 (pod(n)), A306682 (gcd(sigma(n), pod(n))).
%Y A334663 Cf. A334731 (product instead of sum).
%K A334663 nonn
%O A334663 1,2
%A A334663 _Jaroslav Krizek_, May 07 2020