|
%I #24 Jun 22 2024 04:03:51
%S 1,180,1444,12996,23805,36100,52020,60228,64980,68832,95220,301140,
%T 324900,344160,481824,1505700,1718721,1720800,2275758,2409120,3755844,
%U 6874884,6879645,7965153,8593605,11378790,12045600,15930306,17405892
%N 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.
%D Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 180, p. 56, Ellipses, Paris, 2008.
%H Amiram Eldar, <a href="/A081380/b081380.txt">Table of n, a(n) for n = 1..100</a> (terms 1..67 from Donovan Johnson)
%e 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}.
%t 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}]
%o (PARI) is(n)=factor(sigma(n))[,1]==factor(sigma(n,2))[,1] \\ _Charles R Greathouse IV_, Feb 19 2013
%Y Cf. A000203, A001157, A081377, A081378.
%K nonn
%O 1,2
%A _Labos Elemer_, Mar 26 2003
%E More terms from _Lekraj Beedassy_, Jul 18 2008
%E a(16)-a(29) from _Donovan Johnson_, May 24 2009
|
