OFFSET
1,2
COMMENTS
The multiplicities of the divisors are to be ignored.
Is it true that 1 is the only term in both this sequence and A055744? - Farideh Firoozbakht, Jul 01 2008. Answer from Luke Pebody, Jul 10 2008: No! In fact the numbers 103654150315463023813006470 and 6534150553412193640795377701190 are in both sequences.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Prime Puzzles, Puzzle 451
EXAMPLE
n=418=2*11*19: sigma(418)=720, phi[418]=180, common prime factor set ={2,3,5}
k = 477 = 3*3*53: sigma(477) = 702 = 2*3*3*3*13; phi(477) = 312 = 2*2*2*3*13; common factor set: {2,3,13}.
phi(89999)=66528=2^5*3^3*7*11 and sigma(89999)=118272=2^9*3*7*11 so 89999 is in the sequence.
MATHEMATICA
ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] Do[s=ba[DivisorSigma[1, n]]; s1=ba[EulerPhi[n]]; If[Equal[s, s1], k=k+1; Print[n]], {n, 1, 10000}]
PROG
(PARI) is(n)=factor(eulerphi(n=factor(n)))[, 1]==factor(sigma(n))[, 1] \\ Charles R Greathouse IV, Nov 27 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 26 2003
EXTENSIONS
Edited by N. J. A. Sloane, Jul 11 2008 at the suggestion of Farideh Firoozbakht
STATUS
approved