A081380 Numbers k such that the sets of prime factors (ignoring multiplicity) of A000203(k) = sigma(k) and of A001157(k) = sigma_2(k) 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

Author

Labos Elemer, Mar 26 2003

Keywords

• nonn

Examples

			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}.
		

References

• Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 180, p. 56, Ellipses, Paris, 2008.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100 (terms 1..67 from Donovan Johnson)

Crossrefs

Cf. A000203, A001157, A081377, A081378.

Programs

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}]

PARI

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

Extensions

More terms from Lekraj Beedassy, Jul 18 2008

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