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 A061269 Squares with nonzero digits such that (1) each digit is a square and (2) the sum of the digits is a square. 5
 1, 4, 9, 144, 441, 44944 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Note that (1) implies that the product of the digits is a square. Next term, if it exists, is > 90000000000. - Larry Reeves (larryr(AT)acm.org), May 11 2001 REFERENCES Amarnath Murthy, The Smarandache multiplicative square sequence is infinite, (to be published in Smarandache Notions Journal). Amarnath Murthy, Infinitely many common members of the Smarandache additive as well as multiplicative square sequence, (to be published in Smarandache Notions Journal). LINKS Felice Russo, A Set of New Smarandache Functions, Sequences and Conjectures in Number Theory, Lupton, AZ: American Research Press, 2000. EXAMPLE For example, 44944 = 212^2, each digit is a square, sum of digits = 4+4+9+4+4 = 25 = 5^2. MATHEMATICA For[n = 1, n < 100000, n++, a := DigitCount[n^2]; If[a[] == 0, If[a[] == 0, If[a[] == 0, If[a[] == 0, If[a[] == 0, If[a[] == 0, If[a[] == 0, If[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]] == Floor[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]]], Print[n^2]]]]]]]]]] (* Stefan Steinerberger, Mar 15 2006 *) CROSSREFS If zeros are allowed as digits, the result is A061270. A subsequence of A006716. Cf. A053057, A053059, A061267, A061268, A061269, A061270. Sequence in context: A227744 A035127 A061267 * A061271 A084009 A306739 Adjacent sequences:  A061266 A061267 A061268 * A061270 A061271 A061272 KEYWORD nonn,base AUTHOR Amarnath Murthy, Apr 24 2001 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007 STATUS approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)