

A169819


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


3



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
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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. AdamsWatters, 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 * A134681 A218703 A326641
Adjacent sequences: A169816 A169817 A169818 * A169820 A169821 A169822


KEYWORD

base,nonn


AUTHOR

Zak Seidov, May 28 2010


STATUS

approved



