|
| |
|
|
A089496
|
|
mu(prime(n)+1) + mu(prime(n)-1), where mu is the Moebius function.
|
|
3
| |
|
|
-1, 1, 1, 1, 1, 0, 0, 1, -1, -1, 1, -1, -1, 1, 0, 1, 1, -1, -1, 1, -1, 1, 0, 0, -1, -1, 1, -1, -1, 0, -1, -1, -1, 0, 0, 1, 0, 1, -1, 1, -1, -1, 1, 0, 0, 1, -1, 1, -1, 0, -1, 0, 0, -1, 1, 0, 0, 1, -1, -1, 0, 0, -1, 1, -1, 1, 0, 1, 0, -1, 1, -1, -1, 0, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, 1, 0, 0, -1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, -1
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,1
|
|
|
COMMENTS
| This sum is always -1, 0 or 1 because for odd prime p, both p-1 and p+1 cannot be squarefree; one of them will be divisible by 4. This also implies that terms in this sequence are zero only for primes p such that mu(p-1) = mu(p+1) = 0, which is A075432.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Moebius Function
Eric Weisstein's World of Mathematics, Legendre Symbol
|
|
|
FORMULA
| Let p = prime(n), then a(n) = mu(p+(-1/p)), where (-1/p) is the Legendre symbol, A070750. (Pieter Moree)
|
|
|
MATHEMATICA
| Table[MoebiusMu[Prime[n]+1] + MoebiusMu[Prime[n]-1], {n, 2, 150}]
|
|
|
CROSSREFS
| Cf. A089451 (mu(p-1) for prime p), A089495 (mu(p+1) for prime p), A089497 (mu(p+1)-mu(p-1) for prime p).
Sequence in context: A071032 A071034 A089497 * A114592 A140653 A071036
Adjacent sequences: A089493 A089494 A089495 * A089497 A089498 A089499
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Nov 04 2003
|
| |
|
|
