A118548 Squares which are divisible by the product of their digits.

1, 4, 9, 36, 144, 1296, 2916, 11664, 41616, 82944, 186624, 1218816, 2214144, 11614464, 21123216, 21233664, 22127616, 27123264, 49787136, 122943744, 146313216, 171714816, 222129216, 429981696, 812934144, 1316818944

Offset

1,2

Comments

Subsequence of squares in A007602. - Michel Marcus, Aug 24 2014

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 423.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..143

Example

2916 is in the sequence because (1) it is a square, (2) the product of its digits is 2*9*1*6=108 and (3) 2916 is divisible by 108.

Mathematica

sdpdQ[n_]:=Module[{idn=IntegerDigits[n]}, !MemberQ[idn, 0]&&Divisible[ n, Times@@idn]]; Select[Range[40000]^2, sdpdQ] (* Harvey P. Dale, Jul 04 2013 *)

Prog

(Python)
from operator import mul
from functools import reduce
from gmpy2 import t_mod, mpz
A118548 = [n for n in (x**2 for x in range(1, 10**6)) if not (str(n).count('0') or t_mod(n, reduce(mul, (mpz(d) for d in str(n)))))]
# Chai Wah Wu, Aug 23 2014
(PARI) lista(nn) = {for (n=1, nn, sq = n^2; d = digits(sq); p = prod(k=1, #d, d[k]); if (p && !(sq % p), print1(sq, ", ")); ); } \\ Michel Marcus, Aug 24 2014

Crossrefs

Cf. A007602.

Sequence in context: A372211 A227253 A029997 * A176830 A077211 A073977

Adjacent sequences: A118545 A118546 A118547 * A118549 A118550 A118551

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), May 03 2006

Status

approved