A190223 Numbers all of whose divisors are numbers whose decimal digits are noncomposite numbers (1,2,3,5,7).

1, 2, 3, 5, 7, 11, 13, 15, 17, 21, 22, 23, 25, 31, 33, 35, 37, 51, 53, 55, 71, 73, 75, 77, 111, 113, 115, 121, 125, 127, 131, 137, 151, 155, 157, 173, 175, 211, 213, 217, 221, 223, 227, 231, 233, 251, 253, 257, 271, 275, 277, 311, 313, 317, 331, 337, 353

Offset: 1

Author

Jaroslav Krizek, May 06 2011

Keywords

• nonn
• base

Comments

Subset of A001742.

All terms are obviously odd except for 2 and numbers of the form 2*A004022(k). - Harvey P. Dale, May 28 2014 (corrected by Iain Fox, Sep 03 2020)

Examples

			Number 115 is in sequence because all divisors of 115 (1, 5, 23, 115) are numbers whose decimal digits are noncomposite numbers (1,2,3,5,7).
		

Links

• Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from G. C. Greubel)

Crossrefs

Supersequence: A001742.

Cf. A004022, A243534.

Programs

Mathematica

ncnQ[n_]:=Module[{digs=Union[Flatten[IntegerDigits/@Divisors[n]]]}, Complement[ digs,{1,2,3,5,7}]=={}]; Select[ Range[ 400],ncnQ] (* Harvey P. Dale, May 28 2014 *)

PARI

is(k) = fordiv(k, d, if(setminus(vecsort(digits(d), , 8), [1, 2, 3, 5, 7]) != [], return(0))); 1 \\ Iain Fox, Dec 28 2017

Extensions

More terms from Harvey P. Dale, May 28 2014