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

1,2

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)

Links

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

Example

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).

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 *)

Prog

(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

Crossrefs

Supersequence: A001742.

Cf. A004022, A243534.

Sequence in context: A187731 A182140 A240960 * A086070 A117093 A062063

Adjacent sequences: A190220 A190221 A190222 * A190224 A190225 A190226

Keyword

nonn,base

Author

Jaroslav Krizek, May 06 2011

Extensions

More terms from Harvey P. Dale, May 28 2014

Status

approved