|
Search: id:A087625
|
|
|
| A087625 |
|
Number of primes in the ring Z_n. |
|
+0
3
|
|
| 0, 0, 0, 1, 0, 3, 0, 2, 2, 5, 0, 4, 0, 7, 6, 4, 0, 8, 0, 6, 8, 11, 0, 8, 4, 13, 6, 8, 0, 14, 0, 8, 12, 17, 10, 10, 0, 19, 14, 12, 0, 20, 0, 12, 14, 23, 0, 16, 6, 24, 18, 14, 0, 24, 14, 16, 20, 29, 0, 20, 0, 31
(list; graph; listen)
|
|
|
OFFSET
|
1,6
|
|
|
COMMENT
|
a(n) <= n-phi(n)-1.
|
|
FORMULA
|
a(n)=Sum'_{p|n} A087623(p, n), where the sum is over all primes p < n, p | n.
a(p)=0 if p prime.
a(p^k)=p^{k-2}(p-1) if p prime, k>=2.
a(p^k q)=p^{k-2}(p-1)(p+q-1) if p, q primes (q!=p), k>=2.
a(pq)=p+q-2 if p, q primes, p!=q.
A(p^k q^h)=p^{k-2}q^{h-2}(p-1)(q-1)(p+q) if p, q primes (q!=p),
|
|
EXAMPLE
|
a(6)=3 because the three primes in Z_6 are 2,3,4, being 2 and 4 associates. a(500)=5(2-1)(5-1)(2+5)=140.
|
|
CROSSREFS
|
Cf. A087623-A087624, A000010.
Sequence in context: A102003 A004587 A104609 this_sequence A154574 A013307 A119493
Adjacent sequences: A087622 A087623 A087624 this_sequence A087626 A087627 A087628
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 14, 2003
|
|
|
Search completed in 0.002 seconds
|
