

A131187


a(n) = the number of positive integers < n that are neither a divisor of n nor a divisor of (n+1).


1



0, 0, 0, 1, 1, 2, 3, 3, 4, 6, 5, 6, 9, 8, 8, 11, 11, 12, 13, 12, 15, 18, 15, 15, 20, 20, 19, 22, 21, 22, 25, 24, 27, 28, 24, 27, 33, 32, 29, 32, 33, 34, 37, 34, 37, 42, 37, 37, 42, 42, 43, 46, 45, 44, 45, 46, 51, 54, 47, 48, 57, 54, 52, 55, 55, 58, 61, 60, 59, 62, 59, 60, 69, 66
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OFFSET

1,6


LINKS

Table of n, a(n) for n=1..74.


FORMULA

a(n) = n + 2  d(n)  d(n+1), where d(n) is the number of positive divisors of n.


EXAMPLE

The divisors of 9 are 1,3,9. The divisors of 9+1=10 are 1,2,5,10. The 4 positive integers which are < 9 and are neither divisors of 9 nor of 10 are 4,6,7,8. So a(9) = 4.


MAPLE

A131187 := proc(n) local divs ; divs := ( numtheory[divisors](n) union numtheory[divisors](n+1) ) minus {n, n+1} ; n1nops(divs) ; end: seq(A131187(n), n=1..80) ; # R. J. Mathar, Oct 28 2007


CROSSREFS

Cf. A049820.
Sequence in context: A200469 A200251 A207100 * A099072 A257241 A239964
Adjacent sequences: A131184 A131185 A131186 * A131188 A131189 A131190


KEYWORD

nonn,changed


AUTHOR

Leroy Quet, Sep 25 2007


EXTENSIONS

More terms from R. J. Mathar, Oct 28 2007


STATUS

approved



