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%I #14 Nov 23 2022 12:11:00
%S 1,2,3,12,21,122,212,221,364,463,518,537,543,589,661,715,786,969,1111,
%T 1156,1354,1525,1535,1608,1617,1667,1692,1823,1941,2166,2235,2337,
%U 2379,2515,2943,2963,3371,3438,3631,3828,4018,4077,4119,4271,4338,4341,4471
%N Numbers k such that k^2 has property that the sum of its digits and the product of its digits are nonzero squares.
%C See A061267 for the corresponding squares (the so-called ultrasquares). - _M. F. Hasler_, Oct 25 2022
%D Amarnath Murthy, Infinitely many common members of the Smarandache Additive as well as multiplicative square sequence, (To be published in Smarandache Notions Journal).
%D Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000
%e 212^2 = 44944, 4+4+9+4+4 = 25 = 5^2 and 4*4*9*4*4 = 2304 = 48^2.
%o (PARI) select( {is_A061268(n)=vecmin(n=digits(n^2))&&issquare(vecprod(n))&&issquare(vecsum(n))}, [1..4567]) \\ _M. F. Hasler_, Oct 25 2022
%Y Cf. A061267 (the corresponding squares), A053057 (squares with square digit sum), A053059 (squares with square product of digits).
%Y Sequence A061868 allows digit products = 0.
%K nonn,base
%O 1,2
%A _Amarnath Murthy_, Apr 24 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
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