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A379487 a(n) = gcd(n,A003961(n)) * gcd(sigma(n),A276086(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.

%I A379487 #8 Jan 02 2025 13:03:30
%S A379487 1,3,2,1,6,3,2,15,1,9,6,3,2,3,30,1,18,3,10,3,2,9,6,15,1,3,10,1,30,15,
%T A379487 2,21,6,9,42,63,2,15,14,45,42,3,2,21,30,9,6,3,1,3,6,7,18,15,2,15,10,
%U A379487 45,30,105,2,3,2,1,42,3,2,21,6,63,18,45,2,3,10,35,66,21,10,3,1,63,42,21,2,3,30,45,90,15,14,21
%N A379487 a(n) = gcd(n,A003961(n)) * gcd(sigma(n),A276086(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
%H A379487 Antti Karttunen, <a href="/A379487/b379487.txt">Table of n, a(n) for n = 1..20000</a>
%H A379487 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A379487 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%H A379487 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379487 a(n) = A322361(n) * A324644(n).
%o A379487 (PARI)
%o A379487 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A379487 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A379487 A379487(n) = { my(s=sigma(n),x=A003961(n),y=A276086(n)); (gcd(n,x)*gcd(s,y)); };
%Y A379487 Cf. A000203, A003961, A276086, A322361, A324644, A379486, A379488, A379489.
%K A379487 nonn
%O A379487 1,2
%A A379487 _Antti Karttunen_, Jan 02 2025