A342670 a(n) = gcd(n*sigma(A064989(n)), sigma(n)*A064989(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and sigma gives the sum of the divisors of its argument.

1, 1, 1, 1, 2, 6, 2, 1, 1, 2, 4, 4, 2, 12, 36, 1, 2, 6, 2, 2, 2, 4, 4, 24, 1, 6, 5, 56, 6, 72, 2, 1, 24, 2, 120, 28, 2, 12, 4, 10, 2, 12, 2, 4, 36, 8, 4, 8, 1, 1, 18, 2, 6, 30, 8, 24, 2, 6, 6, 144, 2, 12, 2, 1, 12, 144, 2, 14, 12, 240, 4, 12, 2, 2, 9, 4, 336, 24, 2, 2, 1, 2, 4, 56, 4, 12, 24, 4, 6, 72, 56, 8, 2, 8, 360

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = gcd(A342661(n), A342662(n)).

a(n) = gcd(n*A000203(A064989(n)), A000203(n)*A064989(n)).

Prog

(PARI)
A064989(n) = { my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f) };
A326041(n) = sigma(A064989(n));
A342661(n) = (n*A326041(n));
A342662(n) = (sigma(n)*A064989(n));
A342670(n) = gcd(A342661(n), A342662(n));

Crossrefs

Cf. A000203, A064989, A326041, A341530 [ = a(A003961(n))], A342661, A342662, A342663, A342664.

Sequence in context: A004544 A010590 A049061 * A298782 A082516 A318709

Adjacent sequences: A342667 A342668 A342669 * A342671 A342672 A342673

Keyword

nonn

Author

Antti Karttunen, Mar 24 2021

Status

approved