A036433 Number of divisors is a digit in the base 10 representation of n.

1, 2, 14, 23, 29, 34, 46, 63, 68, 74, 76, 78, 88, 94, 116, 127, 128, 134, 138, 141, 142, 143, 145, 146, 164, 182, 184, 186, 189, 194, 196, 211, 214, 223, 227, 229, 233, 236, 238, 239, 241, 247, 248, 249, 251, 254, 257, 258, 261, 263, 268, 269, 271, 274, 277

Offset: 1

Author

Simon Colton (simonco(AT)cs.york.ac.uk)

Keywords

• base
• nice
• nonn

Comments

Invented by the HR concept formation program.

Examples

			14 has 4 divisors and 4 is a digit in the base 10 representation of 14.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
• S. Colton, HR - Automatic Theory Formation in Pure Mathematics

Crossrefs

Cf. A045708, A208272.

Cf. A000005.

Programs

Haskell

a036433 n = a036433_list !! (n-1)
a036433_list = filter f [1..] where
   f x = d < 10 && ("0123456789" !! d) `elem` show x where d = a000005 x
-- Reinhard Zumkeller, Mar 15 2012

Mathematica

Select[Range[300],MemberQ[IntegerDigits[#],DivisorSigma[0,#]]&] (* Harvey P. Dale, Sep 02 2013 *)

Python

from sympy import divisor_count
A036433_list = []
for i in range(1,10**5):
    d = divisor_count(i)
    if d < 10 and str(d) in str(i):
        A036433_list.append(i) # Chai Wah Wu, Jan 07 2015