A093318 - OEIS

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A093318

a(n) = number of positive divisors k of n where mu(k) = 1 and mu(n/k) = -1.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 4, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 4, 1, 1, 0, 4, 1, 0, 1, 0, 1, 1, 0, 4, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,30

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

FORMULA

4*a(n) + Sum_{k|n} mu(k)*mu(n/k) = Product_{p|n} e(p, n), where the product is over the distinct primes dividing n; e(p, n) = 2 if p|n but p^2 does not divide n; e(p, n) = 1 if p^2|n but p^3 does not divide n; e(p, n) = 0 if p^3|n.

MATHEMATICA

a[n_] := DivisorSum[n, 1 &, MoebiusMu[#] == 1 && MoebiusMu[n/#] == -1 &]; Array[a, 100] (* Amiram Eldar, Aug 29 2023 *)

PROG

(PARI) A093318(n) = sumdiv(n, d, ((1==moebius(d))&&((-1)==moebius(n/d)))); \\ Antti Karttunen, Jul 27 2017

CROSSREFS

Cf. A008683 (mu).

Sequence in context: A365952 A324803 A320742 * A255329 A365949 A127560

Adjacent sequences: A093315 A093316 A093317 * A093319 A093320 A093321

KEYWORD

nonn,easy

AUTHOR

Leroy Quet, Apr 26 2004

EXTENSIONS

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 24 2004

STATUS

approved