A081381 Numbers n such that n and tau(n) = A000005(n) have the same prime factors (ignoring multiplicity).

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

Crossrefs

Cf. A000005, A027598, A055744, A065642, A081377-A081380.

Sequence in context: A057529 A336715 A120737 * A235524 A239133 A365517

Adjacent sequences: A081378 A081379 A081380 * A081382 A081383 A081384

Keyword

nonn

Author

Labos Elemer, Mar 26 2003

Status

approved