OFFSET
1,1
COMMENTS
Non-coreful divisor d of a number k is a divisor such that rad(d) != rad(k), where rad(k) is the largest squarefree divisor of k (A007947).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
G. E. Hardy and M. V. Subbarao, Highly powerful numbers, Congress. Numer., Vol. 37 (1983), pp. 277-307. (Annotated scanned copy)
EXAMPLE
60 is in the sequence since its non-coreful divisors are 1, 2, 3, 4, 5, 6, 10, 12, 15, and 20 whose sum is 78 > 60.
MAPLE
with(numtheory): P:=proc(k) local a, n; a:=mul(n, n=factorset(k));
if sigma(k)-a*sigma(k/a)>k then k; fi; end: seq(P(i), i=1..630);
MATHEMATICA
f[p_, e_] := (p^(e + 1) - 1)/(p - 1); fc[p_, e_] := f[p, e] - 1; ncAbQ[n_] := Times @@ (f @@@ FactorInteger[n]) - Times @@ (fc @@@ FactorInteger[n]) > n; Select[Range[2, 1000], ncAbQ]
PROG
(PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
s(n) = my(r=rad(n)); sumdiv(n, d, if (rad(d)!=r, d));
isok(n) = s(n) > n; \\ Michel Marcus, May 14 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar and Paolo P. Lava, May 14 2019
STATUS
approved