cp's OEIS Frontend

A325150 Squares which can be expressed as the product of a number and its reversal in exactly two ways.

%I A325150 #47 May 03 2021 01:26:50
%S A325150 63504,435600,7683984,16240900,25401600,66585600,420332004,558471424,
%T A325150 647804304,726949444,782432784,1067328900,1624090000,1897473600,
%U A325150 2341011456,2540160000,6658560000,50860172484,52587662400,63631071504,67575042304,78384320784,96118600900,106732890000
%N A325150 Squares which can be expressed as the product of a number and its reversal in exactly two ways.
%C A325150 When q = m^2 does not end with a 0 is a term, then m is a palindrome belonging to A117281.
%C A325150 When q = m^2 ending with a 0 is a term, then either m = r * 10^u where r belongs to A325151 and u >= 1, or m is in A342994.
%D A325150 D. Wells, 63504 entry, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1997, p. 168.
%H A325150 Chai Wah Wu, <a href="/A325150/b325150.txt">Table of n, a(n) for n = 1..1672</a>
%H A325150 David A. Corneth, <a href="/A083408/a083408.gp.txt">Examples of factorizations of terms in exactly two or three ways.</a>
%H A325150 Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/eporns.htm">EPRN Numbers</a>.
%e A325150 1) Squares without trailing zeros:
%e A325150 Even square: 7683984 = 2772^2 = 2772 * 2772 = 1584 * 4851.
%e A325150 Odd square: 1239016098321 = 1113111^2 = 1113111 * 1113111 = 1022121 * 1212201.
%e A325150 2) Squares with trailing zeros:
%e A325150 1st case: 16240900 = 4030^2 = 16900 * 961 = 96100 * 169.
%e A325150 2nd case: 435600 = 660^2 = 6600 * 66 = 528 * 825.
%Y A325150 Cf. A325148 (at least one way), A325149 (only one way), A083408 (at least two ways), A307019 (exactly three ways).
%Y A325150 Cf. A083407 (odd squares), A083408 (even squares without trailing 0's).
%Y A325150 Cf. A117281, A325151, A342994.
%K A325150 nonn,base
%O A325150 1,1
%A A325150 _Bernard Schott_, Apr 03 2019
%E A325150 Corrected terms by _Chai Wah Wu_, Apr 12 2019
%E A325150 Definition corrected by _N. J. A. Sloane_, Aug 01 2019