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A333645 a(n) = Sum_{d|n} uphi(d). 0
1, 2, 3, 5, 5, 6, 7, 12, 11, 10, 11, 15, 13, 14, 15, 27, 17, 22, 19, 25, 21, 22, 23, 36, 29, 26, 37, 35, 29, 30, 31, 58, 33, 34, 35, 55, 37, 38, 39, 60, 41, 42, 43, 55, 55, 46, 47, 81, 55, 58, 51, 65, 53, 74, 55, 84, 57, 58, 59, 75, 61, 62, 77, 121, 65, 66, 67, 85, 69, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inverse Moebius transform of A047994.

LINKS

Table of n, a(n) for n=1..70.

FORMULA

G.f.: Sum_{k>=1} uphi(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A023900(d) * A062949(n/d).

MATHEMATICA

uphi[1] = 1; uphi[n_] := Times @@ (#[[1]]^#[[2]] - 1 & /@ FactorInteger[n]); a[n_] := Sum[uphi[d], {d, Divisors[n]}]; Table[a[n], {n, 70}]

A023900[n_] := Sum[MoebiusMu[d] d, {d, Divisors[n]}]; A062949[n_] := Sum[EulerPhi[d] DivisorSigma[0, d], {d, Divisors[n]}]; a[n_] := Sum[A023900[d] A062949[n/d], {d, Divisors[n]}]; Table[a[n], {n, 70}]

PROG

(PARI) uphi(n)=my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1); \\ A047994

a(n) = sumdiv(n, d, uphi(d)); \\ Michel Marcus, Mar 31 2020

CROSSREFS

Cf. A005117 (fixed points), A023900, A047994, A055653, A062949.

Sequence in context: A079114 A058189 A069208 * A066113 A214881 A163831

Adjacent sequences:  A333642 A333643 A333644 * A333646 A333647 A333648

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Mar 31 2020

STATUS

approved

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Last modified September 25 23:23 EDT 2020. Contains 337346 sequences. (Running on oeis4.)