A341530 a(n) = gcd(n*sigma(A003961(n)), sigma(n)*A003961(n)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors of n.

1, 1, 2, 1, 2, 36, 4, 5, 1, 2, 2, 36, 2, 24, 120, 1, 2, 9, 4, 2, 8, 4, 6, 180, 1, 18, 4, 168, 2, 360, 2, 7, 12, 2, 336, 117, 2, 12, 4, 10, 2, 288, 4, 364, 30, 24, 6, 36, 19, 3, 360, 18, 6, 72, 56, 120, 16, 2, 2, 360, 2, 16, 4, 1, 12, 144, 4, 2, 60, 336, 2, 45, 2, 6, 10, 12, 264, 72, 4, 2, 11, 2, 6, 2016, 4, 12, 24

Offset: 1

Author

Antti Karttunen, Feb 16 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A003973, A028982 (positions of odd terms), A341512, A341526, A341527, A341528, A341529, A342670.

Cf. A342674 (same sequence applied onto prime shift array A246278).

Programs

PARI

A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };

Formula

a(n) = gcd(A341528(n), A341529(n)) = gcd(n*A003973(n), A000203(n)*A003961(n)).

a(n) = gcd(A341512(n), A341528(n)) = gcd(A341512(n), A341529(n)) = A342670(A003961(n)). - Antti Karttunen, Mar 24 2021