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

1,1

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.

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 *)

Prog

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

Crossrefs

Cf. A066031, A190882.

Sequence in context: A348275 A138732 A108224 * A232188 A032428 A370795

Adjacent sequences: A268414 A268415 A268416 * A268418 A268419 A268420

Keyword

nonn

Author

Michel Marcus, Feb 04 2016

Status

approved