A061267 - OEIS

%I #15 Nov 23 2022 07:28:00

%S 1,4,9,144,441,14884,44944,48841,132496,214369,268324,288369,294849,

%T 346921,436921,511225,617796,938961,1234321,1336336,1833316,2325625,

%U 2356225,2585664,2614689,2778889,2862864,3323329,3767481,4691556

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

%C 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.

%D Amarnath Murthy, Infinitely many common members of Smarandache Additive as well as Multiplicative Square sequence, (to be published in the Smarandache Notions Journal)

%D Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000

%H Charles R Greathouse IV, <a href="/A061267/b061267.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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 *)

%o (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

%Y Intersection of A050626, A028839, and A000290.

%Y A061869 allows values with zero product.

%Y Cf. A053057, A053059.

%K nonn,base

%O 1,2

%A _Amarnath Murthy_, Apr 24 2001

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