OFFSET
1,2
COMMENTS
Integers m such that A079667(m) is a multiple of m.
Sum_{d|m: 1<=d<=sqrt(m)} (m/d)-d = 0 only when m=1 and Sum_{d|m: 1<=d<=sqrt(m)} (m/d)-d = m only when m=6.
If m is q+1-perfect and 2*Sum_{d|m: 1<=d<=sqrt(m)} d=m then Sum_{d|m: 1<=d<=sqrt(m)} (m/d)-d = m*q or if m is member of this sequence i.e. Sum_{d|m: 1<=d<=sqrt(m)} (m/d)-d = m*q and 2*Sum_{d|m: 1<=d<=sqrt(m)} d=m then m is q+1-perfect.
Does there exist any m apart from 6 which is q+1-perfect, q>=2 and satisfies 2*Sum_{d|m: 1<=d<=sqrt(m)} d=m? Because if it exists then m is member of this sequence.
MATHEMATICA
Select[Range[10^5], Function[m, Mod[DivisorSum[m, Abs[m/# - #] &, # <= Sqrt[m] &], m] == 0]] (* Michael De Vlieger, Mar 17 2021 *)
PROG
(PARI) isok(m) = !(sumdiv(m, d, if (d^2 <= m, m/d-d)) % m); \\ Michel Marcus, Jan 28 2021
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Devansh Singh, Jan 28 2021
STATUS
approved