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

1,2

Comments

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

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A033950, A046754, A046756.

Sequence in context: A307481 A262798 A250431 * A016816 A046756 A143026

Adjacent sequences: A046752 A046753 A046754 * A046756 A046757 A046758

Keyword

nonn

Author

Labos Elemer

Status

approved