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
Keywords
Examples
For k = 352, nusigma(352) = 360. 360 - 352 = 8, which is a nonunitary divisor of 352.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..250
Programs
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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 *) -
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
Comments