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