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Number of divisors is a digit in the base 10 representation of n.
2

%I #22 Jan 08 2015 17:32:01

%S 1,2,14,23,29,34,46,63,68,74,76,78,88,94,116,127,128,134,138,141,142,

%T 143,145,146,164,182,184,186,189,194,196,211,214,223,227,229,233,236,

%U 238,239,241,247,248,249,251,254,257,258,261,263,268,269,271,274,277

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

%C Invented by the HR concept formation program.

%H Reinhard Zumkeller, <a href="/A036433/b036433.txt">Table of n, a(n) for n = 1..10000</a>

%H S. Colton, <a href="http://www.cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2, 1999, #2.

%H S. Colton, <a href="http://web.archive.org/web/20070831060523/http://www.dai.ed.ac.uk/homes/simonco/research/hr/">HR - Automatic Theory Formation in Pure Mathematics</a>

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

%t Select[Range[300],MemberQ[IntegerDigits[#],DivisorSigma[0,#]]&] (* _Harvey P. Dale_, Sep 02 2013 *)

%o (Haskell)

%o a036433 n = a036433_list !! (n-1)

%o a036433_list = filter f [1..] where

%o f x = d < 10 && ("0123456789" !! d) `elem` show x where d = a000005 x

%o -- _Reinhard Zumkeller_, Mar 15 2012

%o (Python)

%o from sympy import divisor_count

%o A036433_list = []

%o for i in range(1,10**5):

%o ....d = divisor_count(i)

%o ....if d < 10 and str(d) in str(i):

%o ........A036433_list.append(i) # _Chai Wah Wu_, Jan 07 2015

%Y Cf. A045708, A208272.

%Y Cf. A000005.

%K base,nice,nonn

%O 1,2

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