OFFSET
1,1
COMMENTS
The nonunitary version of near-perfect numbers (A181595).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..250
EXAMPLE
For k = 352, nusigma(352) = 360. 360 - 352 = 8, which is a nonunitary divisor of 352.
MATHEMATICA
q[n_] := Module[{d = Select[Divisors[n], ! CoprimeQ[#, n/#] &], s}, s = Total[d]; AnyTrue[d, n + # == s &]]; Select[Range[10^4], q] (* Amiram Eldar, May 11 2023 *)
PROG
(PARI) nusigma(n) = {my(f = factor(n)); sigma(f) - prod(i = 1, #f~, f[i, 1]^f[i, 2] + 1); }
is(n) = {my(d = nusigma(n) - n); d > 0 && !(n%d) && gcd(d, n/d) > 1; } \\ Amiram Eldar, May 20 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Jenaro Tomaszewski, May 10 2023
STATUS
approved