A362969 Nonunitary near-perfect numbers: k such that nusigma(k) = k + d where d is a nonunitary divisor of k.

48, 80, 96, 160, 224, 352, 416, 480, 896, 1472, 1476, 1856, 2688, 3968, 6016, 7552, 7808, 8550, 8700, 10332, 17010, 20300, 22496, 36448, 44384, 54944, 63488, 65024, 71264, 73710, 97300, 97792, 114176, 122368, 128512, 310976, 392192, 490496, 515072, 521216, 549990

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

Cf. A048146 (nusigma), A181595.

Sequence in context: A335281 A335196 A348527 * A110229 A108608 A030628

Adjacent sequences: A362966 A362967 A362968 * A362970 A362971 A362972

Keyword

nonn

Author

Jenaro Tomaszewski, May 10 2023

Status

approved