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

Author

Michel Marcus, Mar 20 2015

Keywords

• nonn

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

Examples

			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.
		

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.

Crossrefs

Cf. A055744, A151821.

Cf. A209229.

Programs

Haskell

a256248 n = a256248_list !! (n-1)
a256248_list = filter ((== 1) . a209229 . a055744) [1..]
-- Reinhard Zumkeller, Jun 01 2015

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 *)

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, ", "));););}

Extensions

a(30)-a(45) from Hiroaki Yamanouchi, Mar 31 2015