A061267 Squares whose sum of digits as well as product of digits is a nonzero square.

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

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: A227744 A035127 A354078 * 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