OFFSET
1,1
COMMENTS
The reference considers the sequence {37026, 74052, 81900, ....} with the numbers having at least 4 distinct prime divisors. If k contains two prime divisors only, then k = (p^a)*(q^b), where p and q are two prime distinct divisors, and (p+q)^2 | k => p+q ==0 (mod p) or 0 (mod q), but p==0 (mod q) or q==0 (mod p) is impossible.
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 37026, p. 224, Ellipses,
Paris 2008.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
1575 is in the sequence because the distinct prime divisors of 1575 are {3, 5, 7} and
(3 + 5 + 7)^2 = 225, and 1575 = 225*7.
MAPLE
with(numtheory):for n from 1 to 20000 do:x:=factorset(n):n1:=nops(x):s:=0:for
p from 1 to n1 do: s:=s+x[p]:od:s:=s^2:if n1 >= 2 and irem(n, s)=0 then printf(`%d,
`, n):else fi:od:
MATHEMATICA
ok[k_] := With[{pp = FactorInteger[k][[All, 1]]}, Length[pp] >= 3 && Divisible[k, Total[pp]^2]]; Select[ Range[15000], ok] (* Jean-François Alcover, Sep 23 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, May 23 2011
EXTENSIONS
Definition modified by Harvey P. Dale, Oct 12 2014
STATUS
approved