A081989 Numbers k such that 1 + product of digits of k is a square greater than 1.

3, 8, 13, 18, 24, 31, 35, 38, 42, 46, 53, 57, 64, 68, 75, 79, 81, 83, 86, 97, 113, 118, 124, 131, 135, 138, 142, 146, 153, 157, 164, 168, 175, 179, 181, 183, 186, 197, 214, 222, 226, 234, 238, 241, 243, 246, 258, 262, 264, 283, 285, 311, 315, 318, 324, 328

Offset

1,1

Comments

Sequence is infinite.

Links

Table of n, a(n) for n=1..56.

Example

135 belongs to this sequence as 1*3*5 + 1 = 16 is a square.

Maple

q:= n-> (t-> t>1 and issqr(t))(1+mul(i, i=convert(n, base, 10))):
select(q, [$1..350])[];  # Alois P. Heinz, Nov 20 2025

Mathematica

pdsQ[n_]:=FreeQ[IntegerDigits[n], 0]&&IntegerQ[ Sqrt[ 1+Times@@ IntegerDigits[ n]]]; Select[Range[300], pdsQ] (* Harvey P. Dale, Jul 13 2021 *)

Crossrefs

Cf. A052382, A081990.

Sequence in context: A105502 A105702 A184739 * A264780 A208276 A242487

Adjacent sequences: A081986 A081987 A081988 * A081990 A081991 A081992

Keyword

base,easy,nonn

Author

Amarnath Murthy, Apr 04 2003

Extensions

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

Definition (Name) clarified by Harvey P. Dale, Jul 13 2021

Offset corrected and name further clarified by Sean A. Irvine, Nov 20 2025

Status

approved