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A121041
Number of divisors of n that are also contained in the decimal representation of n.
40
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 3, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 3, 2, 3, 2, 3, 3
OFFSET
1,10
LINKS
FORMULA
a(n) = 1 iff A121042(n) = n.
a(A155005(n)) = n and a(m) < n for m < A155005(n). - Reinhard Zumkeller, Jan 18 2009
EXAMPLE
a(22) = #{2, 22} = 2;
a(23) = #{23} = 1;
a(24) = #{2, 4, 24} = 3.
MATHEMATICA
A121041[n_] := DivisorSum[n, 1 &, StringContainsQ[IntegerString[n], IntegerString[#]] &]; Array[A121041, 150] (* Paolo Xausa, Feb 25 2024 *)
PROG
(Haskell)
import Data.List (isInfixOf)
a121041 n = length $ filter (\d -> n `mod` d == 0
&& show d `isInfixOf` show n) [1..n]
-- Reinhard Zumkeller, Feb 11 2011
(PARI) substr(a, b)=a=digits(a); b=digits(b); for(i=0, #a-#b, for(j=1, #b, if(a[i+j]!=b[j], next(2))); return(1)); 0
a(n)=sumdiv(n, d, substr(n, d)) \\ Charles R Greathouse IV, Mar 31 2016
(Python)
from sympy import divisors
def a(n):
s = str(n)
return sum(1 for d in divisors(n, generator=True) if str(d) in s)
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Jul 11 2022
KEYWORD
nonn,base,easy
AUTHOR
Reinhard Zumkeller, Jul 21 2006
STATUS
approved