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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 04:27 EDT 2021. Contains 343872 sequences. (Running on oeis4.)