A121041 Number of divisors of n that are also contained in the decimal representation of n.

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

Author

Reinhard Zumkeller, Jul 21 2006

Keywords

• nonn
• base
• easy

Examples

			a(22) = #{2, 22} = 2;
a(23) = #{23} = 1;
a(24) = #{2, 4, 24} = 3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040.

Programs

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

Mathematica

A121041[n_] := DivisorSum[n, 1 &, StringContainsQ[IntegerString[n], IntegerString[#]] &]; Array[A121041, 150] (* Paolo Xausa, Feb 25 2024 *)

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

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