

A061267


Squares whose sum of digits as well as product of digits is a nonzero square.


6



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
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OFFSET

1,2


COMMENTS

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.


REFERENCES

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


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

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.


MATHEMATICA

d[n_]:=IntegerDigits[n]; iQ[n_]:=IntegerQ[Sqrt[n]]; Select[Range[2500]^2, iQ[Plus@@(x=d[#])] && iQ[Times@@x] && FreeQ[x, 0] &] (* Jayanta Basu, May 19 2013 *)


PROG

(PARI) is(n)=my(v=digits(n), pr=prod(i=1, #v, v[i])); pr && issquare(pr) && issquare(n) && issquare(sumdigits(n)) \\ Charles R Greathouse IV, May 19 2013


CROSSREFS

Intersection of A050626, A028839, and A000290.
A061869 allows values with zero product. Cf. A053057, A053059.
Sequence in context: A027451 A227744 A035127 * A061269 A061271 A084009
Adjacent sequences: A061264 A061265 A061266 * A061268 A061269 A061270


KEYWORD

nonn,base


AUTHOR

Amarnath Murthy, Apr 24 2001


EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001


STATUS

approved



