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A145551
Numbers k such that product of divisors of k / sum of divisors of k is an integer.
10
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
1,2
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)
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 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Oct 13 2008
EXTENSIONS
90, 96, 108, 126, 132, 140 removed, extended by R. J. Mathar, Oct 14 2008
STATUS
approved