OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is Sum_{n>=1} f(A356871(n)) = 0.0262215..., where f(n) = (6/(Pi^2*n))*Product_{prime p|n}(p/(p+1)). - Amiram Eldar, Sep 02 2022
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
72 is in the sequence since its coreful divisors are 6, 12, 18, 24, 36, 72, whose sum is 168 > 2 * 72.
MATHEMATICA
f[p_, e_] := (p^(e+1)-1)/(p-1)-1; a[1]=1; a[n_] := Times @@ (f @@@ FactorInteger[n]); s={}; Do[If[a[n] > 2n, AppendTo[s, n]], {n, 1, 2000}]; s
PROG
(PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
s(n) = rad(n)*sigma(n/rad(n)); \\ A057723
isok(k) = s(k) > 2*k; \\ Michel Marcus, May 11 2019
(PARI) isok(k) = {my(f=factor(k)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2]+1)-1) / (f[i, 1]-1)-1) > 2*k}; \\ Amiram Eldar, Sep 02 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 10 2019
STATUS
approved