1,2

Note that (1) implies that the product of the digits is a square.

Amarnath Murthy, The Smarandache multiplicative square sequence is infinite. (To be published in Smarandache Notions Journal).

Amarnath Murthy, Infinitely many common members of the Smarandache additive as well as multiplicative square sequence, (To be published in Smarandache Notions Journal).

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

M. L. Perez et al., eds., Smarandache Notions Journal

For example, 44944= 212^2, each digit is a square, sum of digits = 4+4+9+4+4 = 25 = 5^2.

For[n = 1, n < 100000, n++, a := DigitCount[n^2]; If[a[[2]] == 0, If[a[[3]] == 0, If[a[[5]] == 0, If[a[[6]] == 0, If[a[[7]] == 0, If[a[[8]] == 0, If[a[[10]] == 0, If[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]] == Floor[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]]], Print[n^2]]]]]]]]]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 15 2006

If zeros are allowed as digits, the result is A061270.

A subsequence of A006716. Cf. A053057, A053059, A061267, A061268, A061269, A061270.

Sequence in context: A027451 A035127 A061267 this_sequence A061271 A084009 A029738

Adjacent sequences: A061266 A061267 A061268 this_sequence A061270 A061271 A061272

nonn,base

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 24 2001

Next term, if it exists, is > 90000000000 - Larry Reeves (larryr(AT)acm.org), May 11 2001

Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 05 2007