cp's OEIS Frontend

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

%I A145551 #31 Nov 08 2020 05:15:16
%S A145551 1,6,28,30,66,84,102,120,210,270,318,330,364,420,462,496,510,546,570,
%T A145551 642,672,690,714,840,868,870,924,930,966,1080,1092,1122,1320,1410,
%U A145551 1428,1488,1518,1590,1638,1722,1770,1782,1890,1932,2040,2130,2226,2280,2310
%N A145551 Numbers k such that product of divisors of k / sum of divisors of k is an integer.
%C A145551 Numbers k such that A007955(k)/A000203(k) is an integer
%C A145551 Numbers k such that k^sigma_0(k) is a multiple of sigma_1(k)^2. - _Chai Wah Wu_, Mar 09 2016
%H A145551 Amiram Eldar, <a href="/A145551/b145551.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1100 from Paolo P. Lava)
%p A145551 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
%t A145551 spQ[n_]:=Module[{ds=Divisors[n]},IntegerQ[(Times@@ds)/Total[ds]]]; Select[ Range[2500],spQ] (* _Harvey P. Dale_, Jun 26 2012 *)
%t A145551 Select[Range[2500], Divisible[#^(DivisorSigma[0, #]/2), DivisorSigma[1, #]] &] (* _Amiram Eldar_, Nov 08 2020 *)
%o A145551 (Python)
%o A145551 from sympy import divisor_sigma
%o A145551 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
%Y A145551 Cf. A000203, A007955, A140480
%K A145551 easy,nonn
%O A145551 1,2
%A A145551 _Ctibor O. Zizka_, Oct 13 2008
%E A145551 90, 96, 108, 126, 132, 140 removed, extended by _R. J. Mathar_, Oct 14 2008