A076627 a(n) = tau(n)*(n-tau(n)), where tau(n) = number of divisors of n (A000005).

0, 0, 2, 3, 6, 8, 10, 16, 18, 24, 18, 36, 22, 40, 44, 55, 30, 72, 34, 84, 68, 72, 42, 128, 66, 88, 92, 132, 54, 176, 58, 156, 116, 120, 124, 243, 70, 136, 140, 256, 78, 272, 82, 228, 234, 168, 90, 380, 138, 264, 188, 276, 102, 368, 204, 384, 212, 216, 114

Offset: 1

Author

Reinhard Zumkeller, May 27 2003

Keywords

• nonn
• easy

Examples

			a(20) = tau(20)*(20-tau(20)) = 6*(20-6) = 84.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A049820.

Programs

Haskell

a076627 n = a000005 n * a049820 n  -- Reinhard Zumkeller, Feb 06 2012

Maple

with(numtheory): A076627:=n->tau(n)*(n-tau(n)): seq(A076627(n), n=1..100); # Wesley Ivan Hurt, Jul 25 2017

Mathematica

#[[1]](#[[2]]-#[[1]])&/@Table[{DivisorSigma[0,n],n},{n,60}] (* Harvey P. Dale, May 06 2017 *)

PARI

a(n) = my(d = numdiv(n)); d*(n-d); \\ Michel Marcus, Jul 25 2017

Formula

a(n) = A000005(n) * A049820(n). [Reinhard Zumkeller, Feb 06 2012]

Extensions

Wrong offset fixed by Reinhard Zumkeller, Feb 06 2012