

A163001


a(n) = the number of integers k, 1 <= k <= n1, such that p(n)p(k) is divisible by nk (here p(n) = the nth prime.)


1



0, 1, 1, 2, 2, 2, 3, 3, 4, 5, 3, 4, 5, 5, 5, 7, 4, 7, 5, 5, 9, 6, 7, 3, 6, 5, 5, 3, 5, 5, 6, 6, 8, 6, 5, 7, 9, 6, 8, 5, 5, 7, 7, 6, 9, 6, 7, 9, 8, 7, 4, 7, 8, 4, 7, 7, 7, 5, 7, 4, 6, 5, 6, 9, 6, 5, 8, 10, 11, 10, 11, 12, 12, 11, 10, 12, 12, 13, 13, 13, 9, 14, 10, 15, 17, 16, 16, 18, 17, 9, 5, 18, 20
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OFFSET

1,4


LINKS

Table of n, a(n) for n=1..93.


EXAMPLE

The 10th prime is 29. Checking: 292=27 is divisible by 101=9. 293=26 is not divisible by 102=8. 295=24 is not divisible by 103=7. 297=22 is not divisible by 104=6. 2911=18 is not divisible by 105=5. 2913=16 is divisible by 106=4. 2917=12 is divisible by 107=3. 2919=10 is divisible by 108=2. And 2923=6 is divisible by 109=1. There are therefore five k's where p(10)p(k) is divisible by 10k. So a(10)=5.


MAPLE

a := proc (n) local ct, k: ct := 0: for k to n1 do if `mod`(ithprime(n)ithprime(k), nk) = 0 then ct := ct+1 else end if end do: ct end proc: seq(a(n), n = 1 .. 100); # Emeric Deutsch, Jul 30 2009
A163001 := proc(n) local a, k ; a := 0 ; for k from 1 to n1 do if ( ithprime(n)ithprime(k) ) mod (nk) = 0 then a := a+1; fi; od: a ; end ; seq(A163001(n), n=1..120) ; # R. J. Mathar, Jul 30 2009


CROSSREFS

Sequence in context: A240868 A029149 A080570 * A239913 A323701 A226591
Adjacent sequences: A162998 A162999 A163000 * A163002 A163003 A163004


KEYWORD

nonn


AUTHOR

Leroy Quet, Jul 20 2009


EXTENSIONS

Extended by Emeric Deutsch and R. J. Mathar, Jul 30 2009


STATUS

approved



