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A062952 Multiplicative with a(p^e) = (p^(2*e+2)-p^(e+1)-p^e+p)/(p^2-1). 4
1, 4, 9, 18, 25, 36, 49, 78, 87, 100, 121, 162, 169, 196, 225, 326, 289, 348, 361, 450, 441, 484, 529, 702, 645, 676, 807, 882, 841, 900, 961, 1334, 1089, 1156, 1225, 1566, 1369, 1444, 1521, 1950, 1681, 1764, 1849, 2178, 2175, 2116, 2209, 2934, 2443, 2580 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If y is squarefree (cf. A005117(n)) then A062952(y)=y^2. - Benoit Cloitre, Apr 16 2002

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{d|n} phi(d)*sigma(d).

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

MATHEMATICA

f[p_, e_] := (p^(2*e+2)-p^(e+1)-p^e+p)/(p^2-1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 50] (* Amiram Eldar, Jul 31 2019 *)

PROG

(PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d)) \\ Michel Marcus, Jun 17 2013

CROSSREFS

Cf. A057660, A029939.

Sequence in context: A313358 A263351 A064599 * A229027 A100435 A160172

Adjacent sequences:  A062949 A062950 A062951 * A062953 A062954 A062955

KEYWORD

nonn,mult

AUTHOR

Vladeta Jovovic, Jul 21 2001

STATUS

approved

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Last modified August 4 06:22 EDT 2020. Contains 336201 sequences. (Running on oeis4.)