OFFSET
1,1
COMMENTS
Equivalently, numbers that are equal to the sum of their proper infinitary divisors, with one of them taken with a minus sign.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
150 is in the sequence since 150 = 1 + 2 + 3 - 6 + 25 + 50 + 75 is the sum of its proper infinitary divisors with one of them, 6, taken with a minus sign.
MATHEMATICA
fun[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; infDivQ[n_, 1] = True; infDivQ[n_, d_] := BitAnd[IntegerExponent[n, First /@ (f = FactorInteger[d])], (e = Last /@ f)] == e; infAdmQ[n_] := (ab = isigma[n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && infDivQ[n, ab/2]; Select[Range[1000], infAdmQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 18 2020
STATUS
approved