A081380 Numbers n such that the sets of prime factors (ignoring multiplicity) of A000203(n) = sigma(n) and of A001157(n) = sigma_2(n) are identical.

1, 180, 1444, 12996, 23805, 36100, 52020, 60228, 64980, 68832, 95220, 301140, 324900, 344160, 481824, 1505700, 1718721, 1720800, 2275758, 2409120, 3755844, 6874884, 6879645, 7965153, 8593605, 11378790, 12045600, 15930306, 17405892

Offset

1,2

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 180, p. 56, Ellipses, Paris 2008.

Links

Donovan Johnson, Table of n, a(n) for n = 1..67 (terms < 2^31)

Example

n = 1444 = 2^2*19^2, sigma(1444) = 2667 = 3*7*127, sigma_2(1444) = 2744343 = 3^2*7^4*127, common factor set = {3,7,127}.

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]]; s5=ba[DivisorSigma[2, n]]; If[Equal[s, s5], Print[n]], {n, 1, 1000000}]

Prog

(PARI) is(n)=factor(sigma(n))[, 1]==factor(sigma(n, 2))[, 1] \\ Charles R Greathouse IV, Feb 19 2013

Crossrefs

Cf. A000203, A001157, A081377, A081378.

Sequence in context: A251204 A225933 A225932 * A115184 A154672 A211556

Adjacent sequences: A081377 A081378 A081379 * A081381 A081382 A081383

Keyword

nonn

Author

Labos Elemer, Mar 26 2003

Extensions

More terms from Lekraj Beedassy, Jul 18 2008

a(16)-a(29) from Donovan Johnson, May 24 2009

Status

approved