A284375 Numbers whose product of digits is a power of 0.

0, 1, 10, 11, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 120, 130, 140, 150, 160, 170, 180, 190, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 301, 302, 303

Offset: 1

Author

Jaroslav Krizek, Mar 26 2017

Keywords

• nonn
• base

Examples

			111 is in the sequence because 1*1*1 = 1 = 0^0.
		

Crossrefs

Union of A011540 and A002275. Supersequence of A007088.

Cf. Numbers n such that product of digits of n is a power of k for k = 0 - 9: this sequence (k = 0), A002275 (k = 1), A028846 (k = 2), A174813 (k = 3), A284323 (k = 4), A276037 (k = 5), A276038 (k = 6), A276039 (k = 7), A284324 (k = 8), A284295 (k = 9), A328560 (k = 10).

Programs

Magma

Set(Sort([n: n in [1..10000], k in [0..20] | &*Intseq(n) eq 0^k]));

Mathematica

Select[Range[0, 500], Times@@ IntegerDigits[#] <2 &] (* Indranil Ghosh, Mar 26 2017 *)