OFFSET
1,1
COMMENTS
A coreful divisor d of a number k is a divisor with the same set of distinct prime factors as k, or rad(d) = rad(k), where rad(k) is the largest squarefree divisor of k (A007947).
All the terms are odd numbers since the sum of coreful divisors (A057723) of an even number is even.
All the terms are exponentially odd numbers (A268335) since the sum of coreful divisors function is multiplicative and A057723(p^e) = p + p^2 + ... + p^e is even for a prime p and an even exponent e.
None of the terms are coreful Zumkeller numbers (A339979).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
EXAMPLE
1157625 is a term since A057723(1157625) = 2411955 > 2*1157625 and it is odd.
MATHEMATICA
f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[1, 2*10^7, 2], (sum = s[#]) > 2*# && OddQ[sum] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 25 2020
STATUS
approved