A145551 Numbers k such that product of divisors of k / sum of divisors of k is an integer.

1, 6, 28, 30, 66, 84, 102, 120, 210, 270, 318, 330, 364, 420, 462, 496, 510, 546, 570, 642, 672, 690, 714, 840, 868, 870, 924, 930, 966, 1080, 1092, 1122, 1320, 1410, 1428, 1488, 1518, 1590, 1638, 1722, 1770, 1782, 1890, 1932, 2040, 2130, 2226, 2280, 2310

Offset: 1

Author

Ctibor O. Zizka, Oct 13 2008

Keywords

• easy
• nonn

Comments

Numbers k such that A007955(k)/A000203(k) is an integer

Numbers k such that k^sigma_0(k) is a multiple of sigma_1(k)^2. - Chai Wah Wu, Mar 09 2016

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1100 from Paolo P. Lava)

Crossrefs

Cf. A000203, A007955, A140480

Programs

Maple

A007955 := proc(n) local dvs,d ; dvs := numtheory[divisors](n) ; mul(d,d=dvs) ; end: A000203 := proc(n) local dvs,d ; dvs := numtheory[divisors](n) ; add(d,d=dvs) ; end: isA145551 := proc(n) RETURN(A007955(n) mod A000203(n) = 0) ; end: for n from 1 to 10000 do if isA145551(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Oct 14 2008

Mathematica

spQ[n_]:=Module[{ds=Divisors[n]},IntegerQ[(Times@@ds)/Total[ds]]]; Select[ Range[2500],spQ] (* Harvey P. Dale, Jun 26 2012 *)
Select[Range[2500], Divisible[#^(DivisorSigma[0, #]/2), DivisorSigma[1, #]] &] (* Amiram Eldar, Nov 08 2020 *)

Python

from sympy import divisor_sigma
A145551_list = [n for n in range(1,10**3) if not n**divisor_sigma(n,0) % divisor_sigma(n,1)**2] # Chai Wah Wu, Mar 09 2016

Extensions

90, 96, 108, 126, 132, 140 removed, extended by R. J. Mathar, Oct 14 2008