A190218 -id:A190218 - cp's OEIS frontend

A190221 Numbers all of whose divisors are numbers whose decimal digits are in nondecreasing order.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 125

Offset: 1

Jaroslav Krizek, May 06 2011

Subset of A009994. Superset of A028864, A190218 and A190217.

			Number 112 is in sequence because all divisors of 112 (1, 2, 4, 7, 8, 14, 16, 28, 56, 112) are numbers whose decimal digits are in nondecreasing order.

Nathaniel Johnston, Table of n, a(n) for n = 1..1000

with(numtheory): A190221 := proc(n) option remember: local d, dd, i, j, k, m, poten: if(n=1)then return 1: fi: for k from procname(n-1)+1 do d:=divisors(k): poten:=1: for i from 1 to nops(d) do m:=10: dd:=convert(d[i], base, 10): for j from 1 to nops(dd) do if(m>=dd[j])then m:=dd[j]: else poten:=0: break: fi: od: if(poten=0)then break:fi: od: if(poten=1)then return k: fi: od: end: seq(A190221(n), n=1..64); # Nathaniel Johnston, May 06 2011

ndoQ[n_]:=Min[Differences[IntegerDigits[n]]]>=0; Select[Range[ 200],AllTrue[ Divisors[#],ndoQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 02 2021 *)

A211772 Nonprime numbers all of whose divisors are numbers whose decimal digits are in ascending order.

Original entry on oeis.org

1, 4, 6, 8, 9, 12, 14, 15, 16, 18, 24, 25, 26, 27, 28, 34, 35, 36, 38, 39, 45, 46, 48, 49, 56, 57, 58, 68, 69, 78, 125, 134, 135, 136, 138, 145, 158, 169, 178, 235, 237, 245, 247, 259, 267, 268, 278, 289, 356, 358, 469, 478, 578, 1345, 1357, 1369, 2479, 2569

Offset: 1

Jaroslav Krizek, May 07 2012

Sequence is finite with 63 terms, last term is a(63) = 134689.

Complement of A052015 with respect to A190218. Subsequence of A211771.

			Divisors of 24589: 1, 67, 367, 24589 (all divisors with digits in ascending order).

Jaroslav Krizek, Table of n, a(n) for n = 1..63 (complete list).

Cf. A052015 (primes with distinct digits in ascending order), A190218 (numbers all of whose divisors are numbers whose decimal digits are in ascending order), A211771 (nonprime numbers with distinct digits in ascending order).

cp's OEIS Frontend

A190221 Numbers all of whose divisors are numbers whose decimal digits are in nondecreasing order.

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