A169819 a(n) = total number of distinct divisors of n and all of its substrings.

1, 2, 2, 3, 2, 4, 2, 4, 3, 5, 2, 6, 3, 5, 4, 7, 3, 8, 4, 7, 5, 4, 4, 8, 4, 6, 6, 7, 5, 9, 3, 7, 4, 6, 5, 9, 4, 7, 5, 9, 4, 9, 5, 6, 8, 7, 5, 10, 7, 7, 5, 7, 4, 10, 4, 11, 6, 7, 5, 13, 5, 6, 8, 9, 7, 8, 6, 9, 7, 9, 3, 13, 4, 6, 7, 9, 4, 11, 5, 11, 8, 6, 6, 13, 7, 8, 8, 8, 7, 13, 6, 8, 5, 7, 6, 13, 5, 10, 6

Offset

1,2

Comments

Note that we are counting 0 when it occurs as a digit of n, but are not counting any other integers as divisors of 0. (If we did, there would be infinitely many of them; every integer divides 0.) [From Franklin T. Adams-Watters, May 29 2010]

Links

Table of n, a(n) for n=1..99.

Example

a(56) = 11 because divisors of 56 are d1= {1, 2, 4, 7, 8, 14, 28, 56}; 56 has two substrings 5,6; divisors of 5 are d2= {1, 5}, and divisors of 6 are d3= {1, 2, 3,6} ; union of d1,d2,d3 gives 11 distinct divisors of 56 and all of its substrings: {1, 2, 3, 4, 5, 6, 7, 8, 14, 28, 56}.

Mathematica

Table[id = IntegerDigits[n]; FLA = Flatten[Table[Partition[id, k, 1], {k, Length[id]}], 1]; fd = Union[FromDigits /@ FLA]; dv = Length[Union[Flatten[Divisors /@ fd]]], {n, 200}]

Crossrefs

Cf. A177834

Sequence in context: A326198 A324105 A328871 * A373738 A134681 A218703

Adjacent sequences: A169816 A169817 A169818 * A169820 A169821 A169822

Keyword

base,nonn

Author

Zak Seidov, May 28 2010

Status

approved