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Search: id:A061267
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| A061267 |
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Squares whose sum of digits as well as product of digits is a nonzero square. |
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+0
6
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| 1, 4, 9, 144, 441, 14884, 44944, 48841, 132496, 214369, 268324, 288369, 294849, 346921, 436921, 511225, 617796, 938961, 1234321, 1336336, 1833316, 2325625, 2356225, 2585664, 2614689, 2778889, 2862864, 3323329, 3767481, 4691556
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The squares of 969, 9669, 96669, 966669, ... with n 6s belong to this sequence if n = 4*m^2 - 3. The sum of the digits of this number is 36*m^2 and the product of the digits is 108^2 * 20^k, where k = 4xm^2.
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REFERENCES
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Amarnath Murthy, Infinitely many common members of Smarandache Additive as well as Multiplicative Square sequence, (to be published in the Smarandache Notions Journal)
Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000
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LINKS
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M. L. Perez et al., eds., Smarandache Notions Journal
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EXAMPLE
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14884=122^2 is a member of this sequence as 1+4+8+8+4 = 25= 5^2 and 1*4*8*8*4 =1024=32^2.
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CROSSREFS
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A061869 allows values with zero product. Cf. A053057, A053059.
Sequence in context: A128524 A027451 A035127 this_sequence A061269 A061271 A084009
Adjacent sequences: A061264 A061265 A061266 this_sequence A061268 A061269 A061270
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KEYWORD
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nonn,base
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 24 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
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