A046755 Numbers k such that d(k)^3 divides k.

1, 625, 6561, 21952, 32768, 64000, 98304, 117649, 163840, 229376, 360448, 425984, 557056, 622592, 753664, 950272, 1015808, 1212416, 1343488, 1362944, 1409024, 1540096, 1736704, 1933312, 1998848, 2195456, 2326528, 2392064, 2588672

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

Proper subset of both A033950 and A046754. If two terms in the sequence are coprime then their product is also in the sequence.

Examples

			If k = 21952, d(k) = sigma(0,k) = 28. Its 3rd power is 21952, which divides k.
a(103) = 14385152 = (2^15)*439 with 32 divisors and 14385152/(32^3) = 439; 2^15*prime is a typical form of terms in the sequence that have 32 divisors.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)

Crossrefs

Cf. A033950, A046754, A046756.

Programs

Mathematica

Select[ Range[ 1, 14500000 ], IntegerQ[ #/(DivisorSigma[ 0, # ])^3 ]& ]