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

1,2

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

Links

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

Example

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

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 *)

Crossrefs

Disjoint union of A045707 and A206288.

Cf. A000005, A355592, A357299, A357300.

Cf. A004615 (with last digit)

Sequence in context: A262731 A087201 A068492 * A306661 A045707 A032591

Adjacent sequences: A206284 A206285 A206286 * A206288 A206289 A206290

Keyword

nonn,base

Author

Jaroslav Krizek, Feb 12 2012

Status

approved