A129498 Unitary abundancy of n-th unitary abundant number: usigma(k)-2k if this is > 0.

12, 12, 12, 4, 12, 12, 12, 12, 12, 12, 12, 156, 12, 12, 12, 12, 12, 12, 204, 12, 12, 228, 12, 120, 12, 12, 228, 12, 12, 276, 12, 252, 300, 12, 12, 12, 180, 12, 12, 120, 12, 348, 300, 12, 12, 12, 188, 120, 12, 324, 12, 12, 48, 300, 420, 12, 12, 196, 72, 444, 12, 372

Offset

1,1

Comments

The transforms of this sequence are discussed in A129499.

Links

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

Eric Weisstein's World of Mathematics, Unitary Divisor.

Formula

A034448(k)-2k = A034460(k)-k, whenever these are positive.

a(n) = A129468(A034683(n)). - Amiram Eldar, Jun 18 2019

Example

The fourth unitary abundant number is 70. As the unitary divisors of 70 are 1, 2, 5, 7, 10, 14, 35 and 70, we have a(4) = 1+2+5+7+10+14+35+70-2 * 70 = 4.

Mathematica

uab[1]=-1; uab[n_] := Times @@ (1 + Power @@@ FactorInteger[n]) - 2n; seq={}; Do[u=uab[n]; If[u>0, AppendTo[seq, u]], {n, 1, 1000}]; seq (* Amiram Eldar, Jun 18 2019 *)

Crossrefs

Cf. A034448, A034460, A129468, A034683, A129499.

Sequence in context: A268916 A362236 A069873 * A010851 A343194 A123896

Adjacent sequences: A129495 A129496 A129497 * A129499 A129500 A129501

Keyword

easy,nonn

Author

Ant King, Apr 20 2007

Status

approved