daniel
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 Feb 6 revised Does anyone recognize this sequence? removed self-reference Jan 26 revised Brun's sieve bounds deleted 23 characters in body Jan 24 revised Brun's sieve bounds added 21 characters in body Jan 24 revised Brun's sieve bounds deleted 1 character in body Jan 24 revised Brun's sieve bounds added 112 characters in body Jan 24 revised Brun's sieve bounds added 3440 characters in body Jan 22 revised Brun's sieve bounds deleted 782 characters in body Jan 22 revised Brun's sieve bounds deleted 20 characters in body Jan 22 revised Brun's sieve bounds deleted 5 characters in body Jan 21 answered Brun's sieve bounds Jan 18 comment Proof of inequality involving multiplicative function? Terms in the binomial expressions on the left with m factors are all covered by terms in mth powers of the expression on the right. Once we see the LHS can be written as a product of binomials we can compare the two sides. Your hint prompted me to look at the LHS again. The key (which I forgot or didn't know) is that $n=p_k\#,~\binom{k}{m}$ is the number of squarefree divisors of n having $\nu(d)=m.$ Jan 15 accepted Proof of inequality involving multiplicative function? Jan 14 revised Proof of inequality involving multiplicative function? deleted 49 characters in body Jan 14 revised Proof of inequality involving multiplicative function? deleted 204 characters in body Jan 14 revised Proof of inequality involving multiplicative function? added 8 characters in body Jan 14 revised Proof of inequality involving multiplicative function? added 8 characters in body Jan 14 revised Proof of inequality involving multiplicative function? deleted 4 characters in body Jan 14 comment Proof of inequality involving multiplicative function? @user1952009: edited to reflect that. Jan 14 revised Proof of inequality involving multiplicative function? added 10 characters in body Jan 14 revised Proof of inequality involving multiplicative function? edited title