A061270 -id:A061270 - cp's OEIS frontend

A061269 Squares with nonzero digits such that (1) each digit is a square and (2) the sum of the digits is a square.

1, 4, 9, 144, 441, 44944

Offset: 1

Amarnath Murthy, Apr 24 2001

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

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

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

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, Lupton, AZ: American Research Press, 2000.

If zeros are allowed as digits, the result is A061270.
A subsequence of A006716.
Cf. A053057, A053059, A061267, A061268, A061269, A061270.

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, Mar 15 2006 *)

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007

A061272 Squares such that (1) each digit is a square, (2) the sum of squares of the digits is a square.

Original entry on oeis.org

0, 1, 4, 9, 100, 400, 900, 1444, 10000, 40000, 90000, 144400, 1000000, 4000000, 9000000, 14440000, 94109401, 100000000, 400000000, 900000000, 1444000000, 9410940100, 10000000000, 10100049001, 40000000000, 90000000000, 144400000000, 414441100441, 941094010000

Offset: 1

Amarnath Murthy, Apr 24 2001

			1444 = 38^2, each digit is a square, Sum of the squares of digits = 1+16+16+16 = 49 = 7^2.

Amarnath Murthy, Smarandache Pythagoras Additive Square Sequence. (To be published in Smarandache Notions Journal).

Cf. A053057, A053059, A061267, A061268, A061269, A061270, A061090.

okQ[n_]:=Module[{fd=FromDigits[n]},IntegerQ[Sqrt[fd]]&&IntegerQ[ Sqrt[ Total[n^2]]]]; FromDigits/@Select[Tuples[{0,1,4,9},8],okQ] (* Harvey P. Dale, May 12 2011 *)

Corrected and extended by Harvey P. Dale, May 12 2011

More terms from Jason Yuen, Aug 27 2025

cp's OEIS Frontend

A061269 Squares with nonzero digits such that (1) each digit is a square and (2) the sum of the digits is a square.

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