A250004 Numbers representable as x^y + x*y, where x>1, y>1 are integers (without multiplicity).

8, 14, 15, 24, 35, 36, 42, 48, 63, 76, 80, 93, 99, 120, 140, 142, 143, 168, 195, 224, 234, 255, 258, 272, 288, 323, 360, 364, 399, 440, 483, 528, 530, 536, 575, 624, 645, 675, 728, 747, 756, 783, 840, 899, 960, 1023, 1030, 1044, 1088, 1155, 1224, 1295, 1320, 1364, 1368

Offset: 1

Author

Alex Ratushnyak, Jan 14 2015

Keywords

• nonn

Comments

The sequence of numbers representable as x^y + x*y in two or more ways begins: 24, 76, 272, 1044, 2208, 4120, 16412. Example: 2208 = 46^2 + 46*2 = 3^7 + 3*7.

The subsequence of squares begins: 36, 1764.

Examples

			a(2) = 14 = 2^3 + 2*3.
a(3) = 15 = 3^2 + 3*2.
a(22) = 255 = 15^2 + 15*2.
		

Crossrefs

Cf. A253775.

Cf. A024036 is a subsequence, except first 2 terms.

Programs

PARI

isok(n) = {for (p=2, floor(log(n)/log(2)), for (k=2, sqrtnint(n, p), if (n == k^p + p*k, return (1)););); return (0);} \\ Michel Marcus, Jan 16 2015