A257774 - OEIS

%I #12 May 14 2015 17:34:56

%S 1,5,7,6057,292839,1295314,4897814,4967471,5097886,6010324,6919146,

%T 7068165,7189558,9465077,15347958,22842108,24463917,26754863,43378366,

%U 48810128,48885128,50833026,54588458,54649688,68093171,69925865,69980346,73390374,74357144

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

%C 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.

%H Giovanni Resta, <a href="/A257774/b257774.txt">Table of n, a(n) for n = 1..544</a> (terms < 4*10^10)

%e 5 is in the sequence since 5^2 = 25 and 5^3 = 125 and we have 2*5 = 1*2*5 = 10 > 0.

%e 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.

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

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

%K nonn,base

%O 1,2

%A _Pieter Post_, May 08 2015

%E Corrected and extended by _Giovanni Resta_, May 08 2015