

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).


1



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
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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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



