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 A241567 Number of 2-element subsets of {1,...,n} whose sum has more than 3 divisors. 0

%I #4 Apr 27 2014 09:38:46

%S 0,0,0,1,3,5,8,12,17,22,29,36,44,53,62,71,82,94,107,121,135,149,165,

%T 181,198,216,234,253,274,295,317,340,364,388,413,438,464,491,519,547,

%U 577,607,639,672,705,739,775,812,850,889,928,967,1008,1049,1090,1132,1174,1217,1262,1308

%N Number of 2-element subsets of {1,...,n} whose sum has more than 3 divisors.

%C If the constraint on the number of divisors is dropped, one gets A000217 = triangular numbers n*(n+1)/2, which therefore is an upper bound.

%C If one considers 3-element subsets instead, one gets A241564; see the link there for the original motivation.

%C If one considers sums with more than 2 divisors, one gets A241566.

%o (PARI) a(n,m=2,d=3)={s=0;u=vector(m,n,1)~;forvec(v=vector(m,i,[1,n]),numdiv(v*u)>d&&s++,2);s}

%K nonn

%O 1,5

%A _M. F. Hasler_, Apr 25 2014

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Last modified September 7 11:00 EDT 2024. Contains 375730 sequences. (Running on oeis4.)