A331203 Numbers k such that k/(digsum(k)) is an integer cube.

1, 2, 3, 4, 5, 6, 7, 8, 9, 72, 243, 320, 486, 512, 640, 704, 832, 960, 1000, 1088, 1125, 2000, 2401, 3000, 3430, 4000, 4116, 4802, 5000, 5145, 5831, 6000, 6174, 6517, 6860, 7000, 7546, 8000, 8575, 8918, 9000, 9216, 9947, 19683, 35152, 35937, 41743, 43940, 46137

Offset: 1

Author

K. D. Bajpai, Jan 12 2020

Keywords

• nonn
• base

Comments

If m belongs to the sequence, then 1000*m also belongs to the sequence. - Rémy Sigrist, Jan 12 2020

Examples

			a(11) = 243: 243/(2 + 4 + 3) = 27 = 3^3.
a(12) = 320: 320/(3 + 2 + 0) = 64 = 4^3.
		

Crossrefs

Cf. A001102, A005349, A007953, A028839, A059094.

Programs

Magma

[n : n in[1 .. 1000] | IsIntegral((n/(&+Intseq(n)))^(1/3))];

Mathematica

Select[Range[100000], IntegerQ[CubeRoot[#/Total[IntegerDigits[#]]]] &]

PARI

is(n) = my (k=n/sumdigits(n)); type(k)==type(42) && ispower(k,3) \\ Rémy Sigrist, Jan 12 2020