

A293575


Difference between the number of proper divisors of n and the number of squares dividing n.


2



1, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 3, 0, 2, 2, 1, 0, 3, 0, 3, 2, 2, 0, 5, 0, 2, 1, 3, 0, 6, 0, 2, 2, 2, 2, 4, 0, 2, 2, 5, 0, 6, 0, 3, 3, 2, 0, 6, 0, 3, 2, 3, 0, 5, 2, 5, 2, 2, 0, 9, 0, 2, 3, 2, 2, 6, 0, 3, 2, 6, 0, 7, 0, 2, 3, 3, 2, 6, 0, 6, 1, 2, 0, 9, 2, 2, 2, 5, 0, 9, 2, 3, 2, 2, 2, 8, 0, 3, 3, 4, 0, 6, 0, 5, 6
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OFFSET

1,6


COMMENTS

The difference between the number of ways of writing n = m + k and the number of ways of writing n = r*s, where mk and rs.
First occurrence of k beginning with k=1: 1, 2, 8, 6, 12, 36, 24, 30, 72, 96, 60, 2097152, 216, 576, 120, 210, 1152, 240, 864, etc.  Robert G. Wilson v, Nov 28 2017


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A032741(n)  A046951(n).
a(n) = A056595(n)  1.  Antti Karttunen, Oct 30 2017
a(n) = 0 iff n is a prime or a square of a prime, A000430.  Robert G. Wilson v, Nov 28 2017


EXAMPLE

a(6) = 2 because 2 is difference of number of ways of writing n = 1 + 5 = 2 + 4 = 3 + 3 where 15, 24, 33 and number of ways of writing n = 1*6 where 16.


MATHEMATICA

f[n_] := Block[{d = Divisors@ n}, Length@ d  Length[ Select[ d, IntegerQ@ Sqrt@# &]]  1];; Array[f, 105] (* Robert G. Wilson v, Nov 28 2017 *)


CROSSREFS

One less than A056595.
Cf. A000430, A032741, A046951, A166684, A080257.
Sequence in context: A208459 A144764 A084929 * A054014 A158945 A156667
Adjacent sequences: A293572 A293573 A293574 * A293576 A293577 A293578


KEYWORD

sign


AUTHOR

JuriStepan Gerasimov, Oct 14 2017


STATUS

approved



