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.
%I A379488 #9 Jan 02 2025 13:03:34
%S A379488 1,3,3,1,1,3,1,3,3,15,1,1,1,3,15,1,1,3,1,105,3,3,1,15,25,3,15,1,1,3,1,
%T A379488 9,3,3,7,1,1,3,3,45,1,21,1,3,15,3,1,1,7,75,3,1,1,15,5,21,15,3,1,21,1,
%U A379488 3,21,1,7,3,1,9,3,105,1,15,1,3,75,1,7,3,1,15,3,3,1,7,5,3,15,9,1,3,7,3,3,3,1,9,1,147
%N A379488 a(n) = gcd(n,A276086(n)) * gcd(sigma(n),A003961(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
%H A379488 Antti Karttunen, <a href="/A379488/b379488.txt">Table of n, a(n) for n = 1..20000</a>
%H A379488 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A379488 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%H A379488 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379488 a(n) = A324198(n) * A342671(n).
%o A379488 (PARI)
%o A379488 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A379488 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A379488 A379488(n) = { my(s=sigma(n),x=A003961(n),y=A276086(n)); (gcd(n,y)*gcd(s,x)); };
%Y A379488 Cf. A000203, A003961, A276086, A324198, A342671, A379486, A379487, A379489.
%K A379488 nonn
%O A379488 1,2
%A A379488 _Antti Karttunen_, Jan 02 2025