A289276 Numbers k such that phi(k) (the totient function A000010) is a power of the number of divisors of k (A000005).

1, 2, 3, 5, 8, 10, 17, 18, 24, 30, 34, 63, 76, 85, 128, 136, 170, 257, 315, 333, 364, 380, 436, 444, 514, 640, 680, 972, 1285, 1542, 1820, 1824, 1836, 1875, 2142, 2220, 2907, 3285, 3488, 3796, 4369, 4788, 4860

Offset

1,2

Comments

A019434 is a subsequence. - David A. Corneth, Jun 30 2017

Is the frequency of e such that A000005(a(n))^e = A000010(a(n)) finite? - David A. Corneth, Jul 01 2017

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..5319 (first 526 terms from Antti Karttunen)

Mathematica

Join[{1}, Select[Range[2, 5000], IntegerQ[Log[DivisorSigma[0, #], EulerPhi[#]]]&]] (* Harvey P. Dale, Aug 06 2017 *)

Prog

(PARI) ispowerof(n, k)= if(k==1, return(n==1)); while(n>=k, if(n%k!=0, return(0)); n\=k); n==1
isa(n) = ispowerof(eulerphi(n), numdiv(n)) \\ Quick program, fast enough for early values.
(PARI) is(n) = if(n==1, return(1)); my(f = factor(n); phi = eulerphi(f), ndiv = numdiv(f), e = logint(phi, ndiv)); ndiv^e == phi \\ David A. Corneth, Jun 30 2017, changed per suggestion of Charles R Greathouse IV
(PARI) isA289276(n)= if(n==1, return(1)); my(phi = eulerphi(n), ndiv = numdiv(n), v = valuation(phi, ndiv)); ndiv^v == phi; \\ (A variant of above program). - Antti Karttunen, Jun 30 2017
(PARI) list(lim)=my(v=List([1])); forfactored(n=2, lim\1, my(phi = eulerphi(n), ndiv = numdiv(n)); if(ndiv^valuation(phi, ndiv) == phi, listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Jul 01 2017

Crossrefs

Cf. A000005, A000010, A019434, A020488, A032447, A036913, A051281, A068559, A068560, A114063, A286627.

Sequence in context: A246346 A084907 A158724 * A181100 A036961 A122633

Adjacent sequences: A289273 A289274 A289275 * A289277 A289278 A289279

Keyword

nonn,nice

Author

Franklin T. Adams-Watters, Jun 30 2017

Status

approved