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

6, 28, 40, 84, 117, 120, 135, 140, 224, 234, 270, 420, 468, 496, 585, 672, 756, 775, 819, 891, 931, 936, 1080, 1120, 1170, 1287, 1372, 1488, 1550, 1625, 1638, 1782, 1862, 2176, 2299, 2325, 2340, 2480, 2574, 2793, 3100, 3159, 3250, 3276, 3360, 3472

Offset: 1

Author

Benoit Cloitre, Jun 08 2002

Keywords

• easy
• nonn

Comments

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

Examples

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

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000

Crossrefs

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

A000396 (perfect numbers) is a subsequence.

Programs

Mathematica

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

PARI

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

PARI

isok(n) = vecmax(factor(n)[,1]) == vecmax(factor(sigma(n))[,1]); \\ Michel Marcus, Sep 29 2017

Formula

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

n such that A006530(n) = A071190(n). - Michel Marcus, Oct 11 2017