

A081377


Numbers n such that the set of prime divisors of phi(n) is equal to the set of prime divisors of sigma(n).


9



1, 3, 14, 35, 42, 70, 105, 119, 209, 210, 238, 248, 297, 357, 418, 477, 594, 595, 616, 627, 714, 744, 954, 1045, 1178, 1190, 1240, 1254, 1463, 1485, 1672, 1674, 1736, 1785, 1848, 1863, 2079, 2090, 2376, 2385, 2540, 2728, 2926, 2945, 2970, 3080, 3135, 3302
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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*w1], {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

Cf. A000010, A000203, A076533, A065642, A081378, A110751, A110819, A027598, A141718.
Sequence in context: A009394 A076533 A081379 * A050934 A110427 A296294
Adjacent sequences: A081374 A081375 A081376 * A081378 A081379 A081380


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



