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

1,3

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)

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

Prog

(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); };

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).

Sequence in context: A136156 A191657 A155796 * A141238 A094690 A010249

Adjacent sequences: A341527 A341528 A341529 * A341531 A341532 A341533

Keyword

nonn

Author

Antti Karttunen, Feb 16 2021

Status

approved