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

1,1

Comments

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

Links

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

Example

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.

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]

Crossrefs

The nonunitary version of A111592.

Subsequence of A064597.

Similar sequences: A328328, A334972, A334974.

Cf. A048146.

Sequence in context: A260363 A261553 A335281 * A348527 A362969 A110229

Adjacent sequences: A335193 A335194 A335195 * A335197 A335198 A335199

Keyword

nonn

Author

Amiram Eldar, May 26 2020

Status

approved