A268417 Numbers other than prime powers divisible by the sum and the sum of squares of their prime divisors.

99528, 117040, 143520, 199056, 234080, 287040, 288288, 294216, 298584, 349440, 357357, 383040, 398112, 430560, 468160, 574080, 576576, 585200, 588432, 597168, 631488, 698880, 717600, 766080, 796224, 819280, 861120, 864864, 870870, 882648, 895752, 901824, 936320, 957000

Offset: 1

Author

Michel Marcus, Feb 04 2016

Keywords

• nonn

Comments

Intersection of A066031 and A190882.

Prime divisors taken without multiplicity. - Harvey P. Dale, Dec 27 2018

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Jean-Marie de Koninck and Florian Luca, Integers divisible by sums of powers of their prime factors, Journal of Number Theory, Volume 128, Issue 3, March 2008, Pages 557-563.

Crossrefs

Cf. A066031, A190882.

Programs

Mathematica

dssQ[n_]:=Module[{pf=FactorInteger[n][[All,1]]},!PrimePowerQ[ n] && Divisible[ n, Total[pf]]&&Divisible[n,Total[pf^2]]]; Select[ Range[ 960000],dssQ] (* Harvey P. Dale, Dec 27 2018 *)

PARI

isok(n) = my(f = factor(n)[,1]); (#f>2) && ((n % vecsum(f)) == 0) && ((n % sum(k=1, #f, f[k]^2)) == 0);