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 A053635 a(n) = Sum_{d|n} phi(d)*2^(n/d). 15
 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, 4295033472, 8589938808 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..3321 James East and Ron Niles, Integer polygons of given perimeter, arXiv:1710.11245 [math.CO], 2017. James East and Ron Niles, Integer polygons of given perimeter, Bull. Aust. Math. Soc. 100(1) (2019), 131-147. 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 MATHEMATICA a[0] = 0; a[n_] := Sum[EulerPhi[d] 2^(n/d), {d, Divisors[n]}]; Table[a[n], {n, 0, 31}] (* Jean-François Alcover, Aug 30 2018 *) PROG (PARI) a(n) = sumdiv(n, d, eulerphi(d)*2^(n/d)); \\ Michel Marcus, Sep 20 2017 (MAGMA) [0] cat  [&+[EulerPhi(d)*2^(n div d): d in Divisors(n)]: n in [1..40]]; // Vincenzo Librandi, Jul 20 2019 CROSSREFS Cf. A053634, A053636. Twice A034738. Column k=2 of A185651. Sequence in context: A030625 A029929 A222785 * A054061 A294563 A307211 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 September 19 11:26 EDT 2019. Contains 327193 sequences. (Running on oeis4.)