A206287 Numbers with all divisors starting with digit 1.

1, 11, 13, 17, 19, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1111

Offset: 1

Author

Jaroslav Krizek, Feb 12 2012

Keywords

• nonn
• base

Comments

Equivalently, integers m with all divisors starting with the same first digit of m; in fact, as 1 divides all the integers, this digit is necessarily 1; also, for these terms m: A357299(m) = A000005(m). - Bernard Schott, Sep 25 2022

Examples

			All divisors of 187 (1, 11, 17, 187) start with digit 1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Disjoint union of A045707 and A206288.

Cf. A000005, A355592, A357299, A357300.

Cf. A004615 (with last digit)

Programs

Maple

filter:= proc(n) andmap(t -> floor(t/10^ilog10(t)) = 1, numtheory:-divisors(n)) end proc:
select(filter, [seq($10^d .. 2*10^d-1, d=0..3)]); # Robert Israel, Dec 25 2024

Mathematica

fQ[n_] := Module[{d = Divisors[n]}, Union[IntegerDigits[#][[1]] & /@ d] == {1}]; Select[Range[1111], fQ] (* T. D. Noe, Feb 13 2012 *)