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A355815 a(n) = gcd(A276086(n), A277791(n)), where A276086 is primorial base exp-function and A277791 is the denominator of sum of reciprocals of proper divisors of n.

%I A355815 #14 Jul 19 2022 01:13:45
%S A355815 1,1,1,1,1,1,1,1,3,5,1,1,1,1,15,1,1,1,1,5,3,1,1,1,5,1,3,1,1,1,1,1,3,1,
%T A355815 7,1,1,1,3,5,1,7,1,1,15,1,1,1,7,25,3,1,1,1,5,1,3,1,1,1,1,1,21,1,1,1,1,
%U A355815 1,3,35,1,1,1,1,25,1,7,1,1,1,3,1,1,7,5,1,3,1,1,1,7,1,3,1,1,1,1,49,3,5,1,1,1,1,105
%N A355815 a(n) = gcd(A276086(n), A277791(n)), where A276086 is primorial base exp-function and A277791 is the denominator of sum of reciprocals of proper divisors of n.
%H A355815 Antti Karttunen, <a href="/A355815/b355815.txt">Table of n, a(n) for n = 1..11550</a>
%H A355815 Antti Karttunen, <a href="/A355815/a355815.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A355815 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A355815 a(n) = gcd(A276086(n), A277791(n)).
%o A355815 (PARI)
%o A355815 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A355815 A277791(n) = denominator((sigma(n)-1)/n); \\ From A277791
%o A355815 A355815(n) = gcd(A276086(n), A277791(n));
%o A355815 (Python)
%o A355815 from math import gcd
%o A355815 from sympy import nextprime, divisor_sigma
%o A355815 def A355815(n):
%o A355815     m, p, c = 1, 2, n
%o A355815     while c:
%o A355815         c, a = divmod(c,p)
%o A355815         m *= p**a
%o A355815         p = nextprime(p)
%o A355815     return gcd(m,n//gcd(n, divisor_sigma(n)-1)) # _Chai Wah Wu_, Jul 18 2022
%Y A355815 Sequence contains only terms of A048103.
%Y A355815 Cf. A276086, A277791.
%Y A355815 Cf. also A327858, A355003.
%K A355815 nonn
%O A355815 1,9
%A A355815 _Antti Karttunen_, Jul 18 2022