A303356 Unitary deficient-perfect numbers: unitary deficient numbers k such that 2*k-usigma(k) is a unitary divisor of k, where usigma is the sum of unitary divisors of k (A034448).
1, 2, 10, 12, 120, 4080, 5280, 6720, 17472, 137280, 174720, 908160, 29621760, 31100160, 41879040, 89806080, 99240960, 101391360, 143969280, 226652160, 466794240, 732103680, 760488960, 779412480, 916016640, 918382080, 951498240, 1001172480, 1365450240, 3151948800, 9464663040
Offset: 1
Keywords
Examples
120 is in the sequence since 2*120 - usigma(120) = 240 - 216 = 24, and 24 is a unitary divisor of 120.
Programs
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Mathematica
usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; aQ[n_] := Module[{d}, d=2n-usigma[n]; If[ d<=0, False, Divisible[n,d] && GCD[d, n/d] == 1 ]]; Select[Range[100000], aQ]
Extensions
a(19)-a(31) from Giovanni Resta, Apr 26 2018
Comments