A239210 Numbers k such that k^2 is not divisible by any of its nonzero digits.

7, 17, 23, 26, 47, 53, 67, 73, 76, 77, 83, 86, 94, 97, 143, 157, 163, 167, 173, 176, 187, 193, 194, 197, 223, 233, 236, 244, 253, 256, 257, 260, 274, 277, 283, 287, 293, 307, 313, 314, 457, 473, 493, 503, 517, 523, 527, 533, 547, 553, 577, 583, 587, 607, 613

Offset: 1

Author

Colin Barker, Mar 12 2014

Keywords

• nonn
• base

Examples

			53 is a term because 53^2 = 2809 is not divisible by 2, 8 or 9.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A239211, A239212, A239213.

Programs

Mathematica

ndnzQ[n_]:=Count[n^2/Select[IntegerDigits[n^2],#!=0&],?IntegerQ]==0; Select[Range[750],ndnzQ] (* _Harvey P. Dale, Jun 02 2015 *)

PARI

isOK(n) = my(v=vecsort(digits(n^2), , 8)); for(i=1+(v[1]==0), #v, if(n^2%v[i]==0, return(0))); 1
s=[]; for(n=1, 1000, if(isOK(n), s=concat(s, n))); s

Python

def ok(n): return not any(n*n%int(d) == 0 for d in str(n*n) if d != '0')
print(list(filter(ok, range(1, 614)))) # Michael S. Branicky, Jul 17 2021