A241567 - OEIS

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A241567

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

0, 0, 0, 1, 3, 5, 8, 12, 17, 22, 29, 36, 44, 53, 62, 71, 82, 94, 107, 121, 135, 149, 165, 181, 198, 216, 234, 253, 274, 295, 317, 340, 364, 388, 413, 438, 464, 491, 519, 547, 577, 607, 639, 672, 705, 739, 775, 812, 850, 889, 928, 967, 1008, 1049, 1090, 1132, 1174, 1217, 1262, 1308

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OFFSET

1,5

COMMENTS

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.

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

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

LINKS

Table of n, a(n) for n=1..60.

PROG

(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}

CROSSREFS