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

1,10

Links

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

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

Crossrefs

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

Sequence in context: A362663 A089132 A107259 * A157439 A261865 A003589

Adjacent sequences: A121038 A121039 A121040 * A121042 A121043 A121044

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Jul 21 2006

Status

approved