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

1,2

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A176599 A309409 A291687 * A281386 A090817 A357054

Adjacent sequences: A257771 A257772 A257773 * A257775 A257776 A257777

Keyword

nonn,base

Author

Pieter Post, May 08 2015

Extensions

Corrected and extended by Giovanni Resta, May 08 2015

Status

approved