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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.
2
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
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)
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
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