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 A256248 Indices of powers of two in A055744 (the sequence of n that have the same prime power set as phi(n)). 2
 1, 2, 3, 4, 6, 10, 14, 20, 29, 41, 57, 79, 110, 153, 210, 286, 392, 534, 723, 982, 1330, 1790, 2415, 3249, 4359, 5838, 7824, 10457, 13949, 18581, 24724, 32848, 43568, 57723, 76429, 101095, 133599, 176414, 232772, 306920, 404256, 532034, 699655, 919551, 1207627 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All powers of 2, including 1, but excluding 2 itself (A151821) are terms of A055744. This sequence lists the positions of A151821 terms within A055744. Is a(n+1)/a(n) ~ 4/3 for large n? - David A. Corneth, Mar 21 2015 A209229(A055744(a(n))) = 1. - Reinhard Zumkeller, Jun 01 2015 LINKS Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50 Paul Pollack and Carl Pomerance, Prime-Perfect Numbers, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 12a, Paper A14, 2012. EXAMPLE The first terms of A055744 are 1, 4, 8, 16, 18, 32, among which 18 is the only integer that is not a power of 2. Thus this sequence starts with 1, 2, 3, 4, 6. MATHEMATICA t = Select[Range@ 1000000, First /@ FactorInteger@# == First /@ FactorInteger@ EulerPhi@ # &]; f[n_] := Block[{pf = FactorInteger@ n, p2}, p2 = First@ First@ pf; If[Length@ pf == 1 && First@ First@ pf == 2, Last@ First@ pf, 0]]; {1}~Join~Flatten@ Position[f /@ t, n_ /; n > 0] (* Michael De Vlieger, Mar 21 2015 *) PROG (PARI) lista(nn) = {nb = 0; for (n=1, nn, if (factor(n)[, 1]==factor(eulerphi(n))[, 1], nb++; if (n == 2^valuation(n, 2), print1(nb, ", ")); ); ); } (Haskell) a256248 n = a256248_list !! (n-1) a256248_list = filter ((== 1) . a209229 . a055744) [1..] -- Reinhard Zumkeller, Jun 01 2015 CROSSREFS Cf. A055744, A151821. Cf. A209229. Sequence in context: A215255 A200928 A318558 * A089223 A240057 A279467 Adjacent sequences:  A256245 A256246 A256247 * A256249 A256250 A256251 KEYWORD nonn AUTHOR Michel Marcus, Mar 20 2015 EXTENSIONS a(30)-a(45) from Hiroaki Yamanouchi, Mar 31 2015 STATUS approved

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Last modified June 18 15:19 EDT 2021. Contains 345120 sequences. (Running on oeis4.)