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A087625
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Number of primes in the ring Z_n.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| a(n) <= n-phi(n)-1.
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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),
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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.
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CROSSREFS
| Cf. A087623-A087624, A000010.
Sequence in context: A176314 A004587 A104609 * A154574 A119493 A032531
Adjacent sequences: A087622 A087623 A087624 * A087626 A087627 A087628
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KEYWORD
| nonn,easy
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AUTHOR
| Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 14, 2003
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