

A128606


Numbers n such that the product of the squares of digits of n is nonzero and divisible by n.


4



1, 2, 3, 4, 5, 6, 7, 8, 9, 25, 36, 64, 128, 175, 384, 735, 768, 784, 1296, 1764, 2916, 3675, 5625, 7938, 18432, 28672, 34992, 36864, 39366, 46656, 69984, 82944, 96768, 139968, 165375, 236196, 275625, 297675, 354375, 442368, 497664, 524288, 589824, 746496
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OFFSET

1,2


COMMENTS

There are 325 terms below 10^200, with the largest one having 83 decimal digits.  Max Alekseyev, May 31 2018


LINKS

Max Alekseyev, Table of n, a(n) for n = 1..325


MAPLE

P:=proc(n) local i, k, w; for i from 1 by 1 to n do w:=1; k:=i; while k>0 do w:=w*(k(trunc(k/10)*10))^2; k:=trunc(k/10); od; if w>0 then if trunc(w/i)=w/i then print(i); fi; fi; od; end: P(1000000);


MATHEMATICA

fQ[n_] := Block[{d = Times @@ (IntegerDigits[n]^2)}, And[d != 0, Mod[d, n] == 0]]; Select[Range@ 1000000, fQ] (* Michael De Vlieger, Apr 29 2015 *)


PROG

(PARI) for(n=1, 10^6, d=digits(n); p=prod(i=1, #d, d[i]); if(p&&!(p^2%n), print1(n, ", "))) \\ Derek Orr, Apr 29 2015


CROSSREFS

Cf. A007954.
Sequence in context: A096867 A100753 A132416 * A085123 A131571 A179988
Adjacent sequences: A128603 A128604 A128605 * A128607 A128608 A128609


KEYWORD

nonn,base


AUTHOR

Paolo P. Lava and Giorgio Balzarotti, May 08 2007


STATUS

approved



