OFFSET
1,1
COMMENTS
Equivalently, numbers that are equal to the sum of their proper exponential divisors, with one of them taken with a minus sign.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
900 is a term since 900 = 30 + 60 + 90 + 150 - 180 + 300 + 450 is the sum of its proper exponential divisors with one of them, 180, taken with a minus sign.
MATHEMATICA
dQ[n_, m_] := (n > 0 && m > 0 && Divisible[n, m]); expDivQ[n_, d_] := Module[{ft = FactorInteger[n]}, And @@ MapThread[dQ, {ft[[;; , 2]], IntegerExponent[d, ft[[;; , 1]]]}]]; esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; expAdmQ[n_] := (ab = esigma[n] - 2*n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && expDivQ[n, ab/2]; Select[Range[50000], expAdmQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 30 2020
STATUS
approved