A393069 Numbers whose prime divisors all start with the same digit.

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, 53, 58, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 92, 93, 97, 101, 103, 107, 109, 111, 113, 116, 121, 125, 127, 128, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173

Offset

1,2

Comments

All powers of primes are terms.

1 is included, since it has no prime divisors.

Links

Table of n, a(n) for n=1..62.

Example

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

Mathematica

ok[n_] := Length[Union[IntegerDigits[#][[1]] & /@ FactorInteger[n][[All, 1]]]] <= 1
Select[Range[200], ok]

Prog

(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

Crossrefs

Cf. A000961, A206287, A381159.

Sequence in context: A247199 A087441 A326645 * A371445 A325371 A385030

Adjacent sequences: A393066 A393067 A393068 * A393070 A393071 A393072

Keyword

nonn,base

Author

Bartlomiej Pawlik, Apr 30 2026

Status

approved