A333928 Recursive abundant numbers: numbers k such that A333926(k) > 2*k.

12, 18, 20, 30, 36, 42, 60, 66, 70, 78, 84, 90, 100, 102, 108, 114, 120, 126, 132, 138, 140, 144, 150, 156, 168, 174, 180, 186, 196, 198, 204, 210, 220, 222, 228, 234, 240, 246, 252, 258, 260, 270, 276, 282, 294, 300, 306, 308, 318, 324, 330, 336, 340, 342, 348

Offset

1,1

Links

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

Example

12 is a term since A333926(12) = 28 > 2 * 12.

Mathematica

recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; recDivSum[1] = 1; recDivSum[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[350], recDivSum[#] > 2*# &]

Crossrefs

Cf. A333926, A333927.

Analogous sequences: A005101, A034683 (unitary), A064597 (nonunitary), A129575 (exponential), A129656 (infinitary), A292982 (bi-unitary).

Sequence in context: A054753 A098899 A098770 * A357695 A192819 A181487

Adjacent sequences: A333925 A333926 A333927 * A333929 A333930 A333931

Keyword

nonn

Author

Amiram Eldar, Apr 10 2020

Status

approved