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

Author

Amarnath Murthy, Apr 24 2001

Keywords

• nonn
• base

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.

Examples

			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.
		

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

Crossrefs

Intersection of A050626, A028839, and A000290.

A061869 allows values with zero product.

Cf. A053057, A053059.

Programs

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 *)

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

Extensions

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