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A341638 a(n) = Sum_{d|n} phi(d) * sigma(d) * tau(n/d). 1
1, 5, 10, 23, 26, 50, 50, 101, 97, 130, 122, 230, 170, 250, 260, 427, 290, 485, 362, 598, 500, 610, 530, 1010, 671, 850, 904, 1150, 842, 1300, 962, 1761, 1220, 1450, 1300, 2231, 1370, 1810, 1700, 2626, 1682, 2500, 1850, 2806, 2522, 2650, 2210, 4270, 2493, 3355, 2900, 3910, 2810, 4520 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inverse Moebius transform of A062952.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{k=1..n} tau(gcd(n,k)) * sigma(n/gcd(n,k)).

a(n) = Sum_{d|n} A062952(d).

a(n) = Sum_{k=1..n} tau(n/gcd(n,k))*sigma(gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). - Richard L. Ollerton, May 09 2021

MATHEMATICA

Table[Sum[EulerPhi[d] DivisorSigma[1, d] DivisorSigma[0, n/d], {d, Divisors[n]}], {n, 54}]

Table[Sum[DivisorSigma[0, GCD[n, k]] DivisorSigma[1, n/GCD[n, k]], {k, n}], {n, 54}]

PROG

(PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d)*numdiv(n/d)); \\ Michel Marcus, Feb 17 2021

CROSSREFS

Cf. A000005, A000010, A000203, A007430, A062354, A062952, A191831.

Sequence in context: A229440 A067622 A196240 * A280002 A260567 A257464

Adjacent sequences:  A341635 A341636 A341637 * A341639 A341640 A341641

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Feb 16 2021

STATUS

approved

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Last modified January 24 12:29 EST 2022. Contains 350537 sequences. (Running on oeis4.)