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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
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. A209229.
Sequence in context: A200928 A318558 A347867 * A089223 A240057 A279467
KEYWORD
nonn
AUTHOR
Michel Marcus, Mar 20 2015
EXTENSIONS
a(30)-a(45) from Hiroaki Yamanouchi, Mar 31 2015
STATUS
approved