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

1,1

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

Links

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

Formula

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

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

Example

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

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 *)

Prog

(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

Crossrefs

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

A000396 (perfect numbers) is a subsequence.

Sequence in context: A242344 A344588 A247111 * A295078 A055196 A323752

Adjacent sequences: A071831 A071832 A071833 * A071835 A071836 A071837

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 08 2002

Status

approved