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A071834 Numbers n > 1 such that n and sigma(n) have the same largest prime factor. 3

%I

%S 6,28,40,84,117,120,135,140,224,234,270,420,468,496,585,672,756,775,

%T 819,891,931,936,1080,1120,1170,1287,1372,1488,1550,1625,1638,1782,

%U 1862,2176,2299,2325,2340,2480,2574,2793,3100,3159,3250,3276,3360,3472

%N Numbers n > 1 such that n and sigma(n) have the same largest prime factor.

%C By pure convention, we could include a leading 1 to this sequence, as someone using the mathematically arguably value A006530(1) = 1 might search for this sequence with a leading 1. However, this was not done in view of the age of this sequence. - _Rémy Sigrist_, Jan 09 2018

%H Michel Marcus, <a href="/A071834/b071834.txt">Table of n, a(n) for n = 1..1000</a>

%F n such that A006530(n) = A006530(sigma(n)).

%F n such that A006530(n) = A071190(n). - _Michel Marcus_, Oct 11 2017

%e 1550 = 2*5^2*31 and sigma(1550) = 2976 = 2^5*3*31 hence 1550 is in the sequence.

%t fQ[n_] := FactorInteger[n][[-1, 1]] == FactorInteger[DivisorSigma[1, n]][[-1, 1]]; Rest@ Select[ Range@3500, fQ] (* _Robert G. Wilson v_, Jan 09 2018 *)

%o (PARI) for(n=2,1000,if(component(component(factor(n),1),omega(n)) == component(component(factor(sigma(n)),1),omega(sigma(n))), print1(n,",")))

%o (PARI) isok(n) = vecmax(factor(n)[,1]) == vecmax(factor(sigma(n))[,1]); \\ _Michel Marcus_, Sep 29 2017

%Y Cf. A000203 (sigma), A006530 (gpf), A071190.

%Y A000396 (perfect numbers) is a subsequence.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Jun 08 2002

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)