A352584 Numbers k whose decimal representation contains all distinct prime factors of k as substrings.

2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 32, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 125, 127, 128, 131, 135, 137, 139, 149, 151, 157, 163, 167, 173, 175, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 250

Offset: 1

Author

Ivan N. Ianakiev, Mar 21 2022

Keywords

• nonn
• base

Comments

All primes (A000040) and powers of 5 (A000351 without 1) are terms.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000351, A239058 (divisor substrings).

Programs

Mathematica

str[n_]:=ToString/@First/@FactorInteger[n];
fQ[n_]:=Union[Table[StringContainsQ[ToString[n],str[n][[i]]],{i,Length[str[n]]}]]=={True}; Select[Range[2,1000],fQ]
dpfQ[n_]:=Union[SequenceCount[IntegerDigits[n],IntegerDigits[#]]&/@(FactorInteger[n][[;;,1]])] == {1}; Select[Range[2,300],dpfQ] (* Harvey P. Dale, May 30 2023 *)