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

Author

Ant King, Apr 20 2007

Keywords

• easy
• nonn

Comments

The transforms of this sequence are discussed in A129499.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Unitary Divisor.

Crossrefs

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

Programs

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 *)

Formula

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

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