OFFSET
1,2
COMMENTS
Comment from Hugh Montgomery (hlm(AT)umich.edu): I do not recall having seen literature on this question. If p is a prime, p < sqrt(k), then there will be a multiple of p^2 in the block and such a number will then contribute 0. Let Q(M, k) denote the numbers of integers between M+1 and M+k (inclusive) that are not divisible by the square of any prime <= sqrt(k). By the sieve of Eratosthenes-Legendre, Q(M,k) = k/zeta(2) +O(sqrt(k)), uniformly in M. Let Q^+(k) = max_M Q(M,k). I expect that the sum of mu(n) over n = M+1..M+k can be as large as Q^+(k) and as small as -Q^+(k). Indeed, I expect that this could be shown to follow from the prime k-tuple conjecture.
FORMULA
a(n) = max sum m=i...(i+n-1) Mobius(m) over i>=1.
CROSSREFS
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Jun 10 2003
EXTENSIONS
Offset corrected by Eric M. Schmidt, May 07 2013
More terms from Don Reble, Apr 21 2021
STATUS
approved