cp's OEIS Frontend

A342670 a(n) = gcd(n*sigma(A064989(n)), sigma(n)*A064989(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and sigma gives the sum of the divisors of its argument.

%I A342670 #14 Mar 30 2021 18:42:47
%S A342670 1,1,1,1,2,6,2,1,1,2,4,4,2,12,36,1,2,6,2,2,2,4,4,24,1,6,5,56,6,72,2,1,
%T A342670 24,2,120,28,2,12,4,10,2,12,2,4,36,8,4,8,1,1,18,2,6,30,8,24,2,6,6,144,
%U A342670 2,12,2,1,12,144,2,14,12,240,4,12,2,2,9,4,336,24,2,2,1,2,4,56,4,12,24,4,6,72,56,8,2,8,360
%N A342670 a(n) = gcd(n*sigma(A064989(n)), sigma(n)*A064989(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and sigma gives the sum of the divisors of its argument.
%H A342670 Antti Karttunen, <a href="/A342670/b342670.txt">Table of n, a(n) for n = 1..16384</a>
%H A342670 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A342670 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A342670 a(n) = gcd(A342661(n), A342662(n)).
%F A342670 a(n) = gcd(n*A000203(A064989(n)), A000203(n)*A064989(n)).
%o A342670 (PARI)
%o A342670 A064989(n) = { my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f) };
%o A342670 A326041(n) = sigma(A064989(n));
%o A342670 A342661(n) = (n*A326041(n));
%o A342670 A342662(n) = (sigma(n)*A064989(n));
%o A342670 A342670(n) = gcd(A342661(n), A342662(n));
%Y A342670 Cf. A000203, A064989, A326041, A341530 [ = a(A003961(n))], A342661, A342662, A342663, A342664.
%K A342670 nonn
%O A342670 1,5
%A A342670 _Antti Karttunen_, Mar 24 2021