A256248 Indices of powers of two in A055744 (the sequence of n that have the same prime power set as phi(n)).

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

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: A200928 A318558 A347867 * 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