A061867 -id:A061867 - cp's OEIS frontend

A053059 Squares whose product of digits is also a nonzero square.

1, 4, 9, 49, 144, 289, 441, 1444, 7744, 11236, 11449, 11664, 11881, 13689, 14884, 16384, 16641, 19881, 21316, 26896, 28224, 29241, 29929, 31684, 36481, 38416, 41616, 42436, 42849, 43264, 43681, 44944, 48841, 49284, 55696, 69169, 76176

Offset: 1

Felice Russo, Feb 25 2000

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

A061867 allows zeros. Cf. A000290.

nzsQ[n_]:=Module[{pd=Times@@IntegerDigits[n]},pd!=0&&IntegerQ[Sqrt[pd]]]; Select[Range[2000]^2,nzsQ] (* Harvey P. Dale, Nov 13 2012 *)

More terms from James Sellers, Feb 28 2000

A061380 Triangular numbers with product of digits also a triangular number.

Original entry on oeis.org

0, 1, 3, 6, 10, 66, 105, 120, 153, 190, 210, 231, 300, 351, 406, 465, 630, 703, 741, 780, 820, 903, 990, 1035, 1081, 1326, 1540, 1770, 1830, 2016, 2080, 2556, 2701, 2850, 3003, 3081, 3160, 3240, 3403, 3570, 4005, 4095, 4560, 4950, 5050, 5460, 5671, 6105

Offset: 1

Amarnath Murthy, May 02 2001

			153 is a triangular number and the product of digits 15 is also a triangular number.

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A000217, A061867, A069077, A117710.

[t: n in [0..110] | IsSquare(8*p+1) where p is &*Intseq(t) where t is (n*(n+1) div 2)];  // Bruno Berselli, Jun 30 2011

q:= n-> (l-> issqr(1+8*mul(i,i=l)))(convert(n, base, 10)):
select(q, [seq(i*(i+1)/2, i=0..110)])[];  # Alois P. Heinz, Mar 17 2023

tn=Table[n (n+1)/2, {n, 0, 110}] ;Select[tn,MemberQ[tn,Times@@IntegerDigits[#]]&] (* James C. McMahon, Sep 25 2024 *)

isok(k) = ispolygonal(k, 3) && ispolygonal(vecprod(digits(k)), 3); \\ Michel Marcus, Mar 17 2023

More terms from Erich Friedman, May 08 2001

Offset 1 from Michel Marcus, Mar 17 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

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

Robert Israel, Table of n, a(n) for n = 1..10000

A061267 does not allow zero products.

Subsequence of A061867.

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

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 *)

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A053059 Squares whose product of digits is also a nonzero square.

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A061380 Triangular numbers with product of digits also a triangular number.

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica