A393069 - OEIS

%I #16 May 06 2026 21:35:03

%S 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,46,47,49,

%T 53,58,59,61,64,67,71,73,79,81,83,89,92,93,97,101,103,107,109,111,113,

%U 116,121,125,127,128,131,137,139,143,149,151,157,163,167,169,173

%N Numbers whose prime divisors all start with the same digit.

%C All powers of primes are terms.

%C 1 is included, since it has no prime divisors.

%e 46 is a term because 46 = 2*23, and the prime divisors 2 and 23 both begin with digit 2.

%t ok[n_] := Length[Union[IntegerDigits[#][[1]] & /@ FactorInteger[n][[All, 1]]]] <= 1

%t Select[Range[200], ok]

%o (PARI) isok(k) = if(k==1, 1, my(f=factor(k)); #Set(vector(#f~, i, digits(f[i,1])[1])) == 1); \\ _Michel Marcus_, May 01 2026

%Y Cf. A000961, A206287, A381159.

%K nonn,base

%O 1,2

%A _Bartlomiej Pawlik_, Apr 30 2026