A257774 Numbers n such that the products of the decimal digits of n^2 and n^3 coincide, n^2 and n^3 are zeroless.

1, 5, 7, 6057, 292839, 1295314, 4897814, 4967471, 5097886, 6010324, 6919146, 7068165, 7189558, 9465077, 15347958, 22842108, 24463917, 26754863, 43378366, 48810128, 48885128, 50833026, 54588458, 54649688, 68093171, 69925865, 69980346, 73390374, 74357144

Offset: 1

Author

Pieter Post, May 08 2015

Keywords

• nonn
• base

Comments

This sequence is more sporadic than A257760. It appears there is no sequence for zeroless numbers n and n^3 such that the products of the decimal digits coincide, except for the trivial 1.

Examples

			5 is in the sequence since 5^2 = 25 and 5^3 = 125 and we have 2*5 = 1*2*5 = 10 > 0.
6057 is in the sequence since 6057^2 = 36687249 and 6057^3 = 222214667193 and we have 3*6*6*8*7*2*4*9 = 2*2*2*2*1*4*6*6*7*1*9*3 = 435456 > 0.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..544 (terms < 4*10^10)

Crossrefs

Cf. A000290, A000578, A029793, A052382, A257760, A257763.

Programs

Mathematica

pod[n_] := Times@@IntegerDigits@n; Select[Range[10^7], pod[#^3] == pod[#^2] > 0 &] (* Giovanni Resta, May 08 2015 *)

Extensions

Corrected and extended by Giovanni Resta, May 08 2015