A335196 Nonunitary admirable numbers: numbers k such that there is a nonunitary divisor d of k such that nusigma(k) - 2*d = k, where nusigma is the sum of nonunitary divisors function (A048146).

48, 80, 96, 108, 120, 160, 168, 180, 192, 216, 224, 252, 264, 280, 300, 312, 320, 336, 352, 360, 384, 396, 408, 416, 432, 448, 456, 468, 480, 504, 528, 540, 552, 560, 600, 612, 624, 640, 672, 684, 696, 704, 720, 744, 756, 768, 792, 816, 828, 832, 840, 864, 880

Offset: 1

Author

Amiram Eldar, May 26 2020

Keywords

• nonn

Comments

Equivalently, numbers that are equal to the sum of their nonunitary divisors, with one of them taken with a minus sign.

Examples

			48 is a term since 48 = 2 - 4 + 6 + 8 + 12 + 24 is the sum of its nonunitary divisors with one of them, 4, taken with a minus sign.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

The nonunitary version of A111592.

Subsequence of A064597.

Similar sequences: A328328, A334972, A334974.

Cf. A048146.

Programs

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; nuAdmQ[n_] := (ab = nusigma[n] - n) > 0 && EvenQ[ab] && ab/2 < n && !CoprimeQ[ab/2, 2*n/ab]; Select[Range[1000], nuAdmQ]