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A081381
Numbers n such that n and tau(n) = A000005(n) have the same prime factors (ignoring multiplicity).
4
1, 2, 8, 9, 12, 18, 72, 80, 96, 108, 128, 288, 448, 486, 625, 720, 768, 864, 972, 1152, 1200, 1250, 1620, 1944, 2000, 2025, 2560, 4032, 4050, 5000, 5625, 6144, 6561, 6912, 7500, 7776, 8748, 9408, 10800, 11250, 11264, 12960, 13122, 16200, 18000, 18432, 19440
OFFSET
1,2
LINKS
Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..1096 (terms < 10^11, first 500 terms from Donovan Johnson)
EXAMPLE
n = 5000 = 2*2*2*5*5*5*5, tau(5000) = 20 = 2*2*5, common prime factors: {2,5}
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[0, n]]; If[Equal[s, ba[n]], Print[n]], {n, 1, 10000}]
PROG
(PARI) is(n)=my(f=factor(n)); factor(numdiv(f))[, 1]==f[, 1] \\ Charles R Greathouse IV, Oct 19 2017
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 26 2003
STATUS
approved