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A068970 a(n) = Sum_{d|n} phi(d^4). 2
1, 9, 55, 137, 501, 495, 2059, 2185, 4429, 4509, 13311, 7535, 26365, 18531, 27555, 34953, 78609, 39861, 123463, 68637, 113245, 119799, 267675, 120175, 313001, 237285, 358723, 282083, 682893, 247995, 893731, 559241, 732105, 707481, 1031559, 606773, 1823509 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

Also Sum_{d|n} d^m*phi(d^(4-m)) for m=0, 1, 2, 3.

Multiplicative with a(p^e) = 1 + p^3 + (p-1)(p^(4e)-1)/(p^4-1).

G.f.: Sum_{k>=1} k^3*phi(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Mar 10 2018

MAPLE

f:= n -> add(numtheory:-phi(d^4), d=numtheory:-divisors(n)):

map(f, [$1..100]); # Robert Israel, Sep 13 2018

MATHEMATICA

Table[Total[EulerPhi[Divisors[n]^4]], {n, 40}] (* Vincenzo Librandi, Sep 13 2018 *)

PROG

(PARI) a(n) = sumdiv(n, d, eulerphi(d^4)); \\ Michel Marcus, Mar 10 2018

CROSSREFS

Cf. A057660, A068963.

Sequence in context: A058852 A145875 A299519 * A141530 A263478 A016269

Adjacent sequences:  A068967 A068968 A068969 * A068971 A068972 A068973

KEYWORD

easy,nonn,mult

AUTHOR

Benoit Cloitre, Apr 06 2002

STATUS

approved

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Last modified May 24 18:34 EDT 2019. Contains 323534 sequences. (Running on oeis4.)