A206288 Nonprime numbers with all divisors starting with digit 1.

1, 121, 143, 169, 187, 1111, 1133, 1177, 1199, 1243, 1313, 1331, 1339, 1391, 1397, 1417, 1441, 1469, 1507, 1529, 1573, 1639, 1651, 1661, 1703, 1717, 1727, 1751, 1781, 1793, 1807, 1819, 1837, 1853, 1859, 1903, 1919, 1921, 1937, 1957, 1963, 1969, 1991

Offset: 1

Author

Jaroslav Krizek, Feb 12 2012

Keywords

• nonn
• base

Comments

Subsequence of A206286, A131835.

Complement of A045707 (primes with first digit 1) with respect to A202287 (numbers with all divisors starting with digit 1).

Examples

			All divisors of 1859 (1, 11, 13, 169, 1859) start with digit 1.
		

Links

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

Crossrefs

Cf. A045707 (primes with first digit 1), A202287 (numbers with all divisors starting with digit 1).

Programs

Maple

fd1:= n -> n < 2*10^ilog10(n):
filter:= proc(n) not isprime(n) and andmap(fd1,numtheory:-divisors(n)) end proc:
select(filter, [1,seq(seq(i,i=10^d+1..2*10^d-1,2),d=1..3)]); # Robert Israel, Mar 13 2019

Mathematica

fQ[n_] := Module[{d = Divisors[n]}, Union[IntegerDigits[#][[1]] & /@ d] == {1}]; Select[Range[1991], ! PrimeQ[#] && fQ[#] &] (* T. D. Noe, Feb 13 2012 *)