A352584 - OEIS

%I #13 May 30 2023 13:54:11

%S 2,3,5,7,11,13,17,19,23,25,29,31,32,37,41,43,47,53,59,61,67,71,73,79,

%T 83,89,97,101,103,107,109,113,125,127,128,131,135,137,139,149,151,157,

%U 163,167,173,175,179,181,191,193,197,199,211,223,227,229,233,239,241,243,250

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

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

%H Harvey P. Dale, <a href="/A352584/b352584.txt">Table of n, a(n) for n = 1..1000</a>

%t str[n_]:=ToString/@First/@FactorInteger[n];

%t fQ[n_]:=Union[Table[StringContainsQ[ToString[n],str[n][[i]]],{i,Length[str[n]]}]]=={True}; Select[Range[2,1000],fQ]

%t dpfQ[n_]:=Union[SequenceCount[IntegerDigits[n],IntegerDigits[#]]&/@(FactorInteger[n][[;;,1]])] == {1}; Select[Range[2,300],dpfQ] (* _Harvey P. Dale_, May 30 2023 *)

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

%K nonn,base

%O 1,1

%A _Ivan N. Ianakiev_, Mar 21 2022