cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A061268 Numbers k such that k^2 has property that the sum of its digits and the product of its digits are nonzero squares.

Original entry on oeis.org

1, 2, 3, 12, 21, 122, 212, 221, 364, 463, 518, 537, 543, 589, 661, 715, 786, 969, 1111, 1156, 1354, 1525, 1535, 1608, 1617, 1667, 1692, 1823, 1941, 2166, 2235, 2337, 2379, 2515, 2943, 2963, 3371, 3438, 3631, 3828, 4018, 4077, 4119, 4271, 4338, 4341, 4471
Offset: 1

Views

Author

Amarnath Murthy, Apr 24 2001

Keywords

Comments

See A061267 for the corresponding squares (the so-called ultrasquares). - M. F. Hasler, Oct 25 2022

Examples

			212^2 = 44944, 4+4+9+4+4 = 25 = 5^2 and 4*4*9*4*4 = 2304 = 48^2.

References

  • 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

Crossrefs

Cf. A061267 (the corresponding squares), A053057 (squares with square digit sum), A053059 (squares with square product of digits).
Sequence A061868 allows digit products = 0.

Programs

  • PARI
    select( {is_A061268(n)=vecmin(n=digits(n^2))&&issquare(vecprod(n))&&issquare(vecsum(n))}, [1..4567]) \\ M. F. Hasler, Oct 25 2022

Extensions

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

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

Original entry on oeis.org

1, 4, 9, 144, 441, 44944
Offset: 1

Views

Author

Amarnath Murthy, Apr 24 2001

Keywords

Comments

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

Examples

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

References

  • 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).

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

Extensions

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

A061270 Squares such that each digit is a square and the sum of the digits is a square.

Original entry on oeis.org

0, 1, 4, 9, 100, 144, 400, 441, 900, 10000, 10404, 14400, 40000, 40401, 44100, 44944, 90000, 1000000, 1004004, 1040400, 1440000, 4000000, 4004001, 4040100, 4410000, 4494400, 9000000, 9941409, 11909401, 100000000, 100040004, 100400400
Offset: 1

Views

Author

Amarnath Murthy, Apr 24 2001

Keywords

Examples

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

References

  • Amarnath Murthy, Smarandache Additive 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.

Crossrefs

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

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
a(1)=0 inserted by Sean A. Irvine, Jan 29 2023

A061869 Squares whose sum of digits as well as product of digits is a square (allowing zero).

Original entry on oeis.org

0, 1, 4, 9, 100, 144, 400, 441, 900, 2025, 2304, 2601, 3600, 8100, 9025, 10000, 10201, 10404, 10609, 10816, 11025, 12100, 14400, 14884, 16900, 19600, 21904, 22500, 30625, 30976, 32400, 40000, 40401, 40804, 41209, 44100, 44944, 48400, 48841
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

A061267 does not allow zero products.
Subsequence of A061867.

Programs

  • Maple
    filter:= proc(t) local L;
  L:= convert(t,base,10);
  issqr(convert(L,`+`)) and issqr(convert(L,`*`))
end proc:
select(filter, [seq(i^2,i=0..300)]); # Robert Israel, Feb 15 2023
  • Mathematica
    spdQ[n_]:=Module[{idn=IntegerDigits[n]},IntegerQ[Sqrt[Total[idn]]] && IntegerQ[ Sqrt[Times@@idn]]]; Select[Range[300]^2,spdQ] (* Harvey P. Dale, Jan 24 2013 *)

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

Views

Author

Amarnath Murthy, Apr 24 2001

Keywords

Examples

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

References

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

Crossrefs

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

Programs

  • Mathematica
    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 *)

Extensions

Corrected and extended by Harvey P. Dale, May 12 2011
More terms from Jason Yuen, Aug 27 2025
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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