Search: id:A061269
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%I A061269
%S A061269 1,4,9,144,441,44944
%N A061269 Squares with nonzero digits such that (1) each digit is a square and 
               (2) the sum of the digits is a square.
%C A061269 Note that (1) implies that the product of the digits is a square.
%D A061269 Amarnath Murthy, The Smarandache multiplicative square sequence is infinite. 
               (To be published in Smarandache Notions Journal).
%D A061269 Amarnath Murthy, Infinitely many common members of the Smarandache additive 
               as well as multiplicative square sequence, (To be published in Smarandache 
               Notions Journal).
%D A061269 Felice Russo, A set of new Smarandache functions, sequences and conjectures 
               in number theory, American Research Press 2000
%H A061269 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%e A061269 For example, 44944= 212^2, each digit is a square, sum of digits = 4+4+9+4+4 
               = 25 = 5^2.
%t A061269 For[n = 1, n < 100000, n++, a := DigitCount[n^2]; If[a[[2]] == 0, If[a[[3]] 
               == 0, If[a[[5]] == 0, If[a[[6]] == 0, If[a[[7]] == 0, If[a[[8]] == 
               0, If[a[[10]] == 0, If[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]] == Floor[Sqrt[Sum[a[[i]]*i, 
               {i, 1, 10}]]], Print[n^2]]]]]]]]]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Mar 15 2006
%Y A061269 If zeros are allowed as digits, the result is A061270.
%Y A061269 A subsequence of A006716. Cf. A053057, A053059, A061267, A061268, A061269, 
               A061270.
%Y A061269 Sequence in context: A027451 A035127 A061267 this_sequence A061271 A084009 
               A029738
%Y A061269 Adjacent sequences: A061266 A061267 A061268 this_sequence A061270 A061271 
               A061272
%K A061269 nonn,base
%O A061269 1,2
%A A061269 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 24 2001
%E A061269 Next term, if it exists, is > 90000000000 - Larry Reeves (larryr(AT)acm.org), 
               May 11 2001
%E A061269 Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion 
               of Andrew Plewe, Jun 05 2007

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