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Total number of elements in all primitive subsets of the integers 1 to n.
4

%I #15 Jun 27 2022 10:50:24

%S 0,1,2,5,8,21,29,73,105,193,288,677,853,1957,2961,4913,6809,15145,

%T 19605,43105,57889,98849,151457,327505,397825,784945,1201189,2009229,

%U 2772729,5901185,7364945,15609825,21206049,36440033,55602033,105010513,127336513,267374561

%N Total number of elements in all primitive subsets of the integers 1 to n.

%C A primitive set has no element that divides another element in the same set.

%D R. K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, New York, (1994).

%H Fausto A. C. Cariboni, <a href="/A087077/b087077.txt">Table of n, a(n) for n = 0..75</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimitiveSequence.html">Primitive Sequence</a>.

%F a(n) = Sum_{k=1..ceiling(n/2)} k * A355145(n,k). - _Alois P. Heinz_, Jun 27 2022

%e a(4)=8 since the primitive subsets of (1,2,3,4) are ( ) (1) (2) (3) (4) (2,3) (3,4) and these contain eight elements

%Y A051026 gives the number of primitive subsets. A087078 gives the sum of the elements of the primitive subsets. A087080 gives the number elements in the coprime subsets.

%Y Cf. A355145.

%K nonn

%O 0,3

%A Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 10 2003

%E Terms a(34)-a(37) from _Fausto A. C. Cariboni_, Feb 02 2022