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A053635 a(n) = Sum_{d|n} phi(d)*2^(n/d). 12
0, 2, 6, 12, 24, 40, 84, 140, 288, 540, 1080, 2068, 4224, 8216, 16548, 32880, 65856, 131104, 262836, 524324, 1049760, 2097480, 4196412, 8388652, 16782048, 33554600, 67117128, 134218836, 268452240, 536870968, 1073777040, 2147483708 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..31.

James East, Ron Niles, Integer polygons of given perimeter, arXiv:1710.11245 [math.CO], 2017.

T. Pisanski, D. Schattschneider and B. Servatius, Applying Burnside's lemma to a one-dimensional Escher problem, Math. Mag., 79 (2006), 167-180. See v(n).

FORMULA

a(n) = n * A000031(n).

MAPLE

with(numtheory); A053685:=n->add( phi(n/d)*2^d, d in divisors(n)); # N. J. A. Sloane, Nov 21 2009

PROG

(PARI) a(n) = sumdiv(n, d, eulerphi(d)*2^(n/d)); \\ Michel Marcus, Sep 20 2017

CROSSREFS

Cf. A053634, A053636. Twice A034738.

Column k=2 of A185651.

Sequence in context: A030625 A029929 A222785 * A054061 A294563 A294545

Adjacent sequences:  A053632 A053633 A053634 * A053636 A053637 A053638

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 23 2000

STATUS

approved

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Last modified February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)