

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.


2



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
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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 A198875
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



