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A334663 a(n) = Sum_{d|n} gcd(sigma(d), pod(d)), where pod(k) is the product of the divisors of k (A007955). 4
1, 2, 2, 3, 2, 15, 2, 4, 3, 5, 2, 20, 2, 7, 6, 5, 2, 19, 2, 8, 4, 7, 2, 33, 3, 5, 4, 64, 2, 93, 2, 6, 6, 5, 4, 25, 2, 7, 4, 19, 2, 69, 2, 12, 10, 7, 2, 38, 3, 7, 12, 8, 2, 44, 4, 73, 4, 5, 2, 124, 2, 7, 6, 7, 4, 167, 2, 8, 6, 27, 2, 41, 2, 5, 8, 12, 4, 43, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Inverse Möbius transform of A306682. - Antti Karttunen, May 09 2020
LINKS
FORMULA
a(p) = 2 for p = primes (A000040).
EXAMPLE
a(6) = gcd(sigma(1), pod(1)) + gcd(sigma(2), pod(2)) + gcd(sigma(3), pod(3)) + gcd(sigma(6), pod(6)) = gcd(1, 1) + gcd(3, 2) + gcd(4, 3) + gcd(12, 36) = 1 + 1 + 1 + 12 = 15.
PROG
(Magma) [&+[GCD(&+Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, gcd(sigma(d), vecprod(divisors(d)))); \\ Michel Marcus, May 08 2020
CROSSREFS
Cf. A334579 (Sum_{d|n} gcd(tau(d), sigma(d))), A334662 (Sum_{d|n} gcd(tau(d), pod(d))).
Cf. A000203 (sigma(n)), A007955 (pod(n)), A306682 (gcd(sigma(n), pod(n))).
Cf. A334731 (product instead of sum).
Sequence in context: A016007 A226410 A226340 * A016008 A334514 A363001
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, May 07 2020
STATUS
approved

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Last modified June 23 14:31 EDT 2024. Contains 373651 sequences. (Running on oeis4.)