

A082552


Number of sets of distinct primes, the greatest of which is prime(n), whose arithmetic mean is an integer.


1



1, 1, 2, 5, 6, 12, 21, 31, 58, 111, 184, 356, 665, 1223, 2260, 4227, 7930, 15095, 28334, 53822, 102317, 195012, 373001, 714405, 1370698, 2633383, 5067643, 9765457, 18846711, 36413982, 70431270, 136391723, 264384100, 512959093, 996173830
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OFFSET

1,3


COMMENTS

The sum of the first 23 primes gives 874 = 23*38, see A045345.  Alois P. Heinz, Aug 02 2009


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..100


EXAMPLE

a(4) = 5: prime(4) = 7 and the five sets are (5+7)/2 = 6, 7/1 = 7, (3+7)/2 = 5, (2+3+7)/3 = 4, (3+5+7)/3 = 5.


MAPLE

b:= proc(t, i, m, h) option remember; if h=0 then `if` (t=0, 1, 0) elif i<1 or h>i then 0 else b (t, i1, m, h) +b((t+ithprime(i)) mod m, i1, m, h1) fi end: a:= n> add(b(ithprime(n) mod m, n1, m, m1), m=1..n): seq (a(n), n=1..40); # Alois P. Heinz, Aug 02 2009


MATHEMATICA

f[n_] := Block[{c = 0, k = n, lst = Prime@ Range@n, np = Prime@n, slst}, While[k < 2^n, slst = Subsets[lst, All, {k}]; If[Last@slst == np && Mod[Plus @@ slst, Length@slst] == 0, c++ ]; k++ ]; c]; Do[ Print[{n, f@n} // Timing], {n, 24}] (* Robert G. Wilson v *)


CROSSREFS

Cf. A051293, A072701.
Sequence in context: A108365 A064765 A257805 * A243798 A057683 A277012
Adjacent sequences: A082549 A082550 A082551 * A082553 A082554 A082555


KEYWORD

nonn


AUTHOR

Naohiro Nomoto, May 03 2003


EXTENSIONS

a(22)a(24) from Robert G. Wilson v, Jan 19 2007
Corrected a(23) and extended by Alois P. Heinz, Aug 02 2009


STATUS

approved



