A082552 Number of sets of distinct primes, the greatest of which is prime(n), whose arithmetic mean is an integer.

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

Offset: 1

Author

Naohiro Nomoto, May 03 2003

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A051293, A072701.

Programs

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, i-1, m, h) +b((t+ithprime(i)) mod m, i-1, m, h-1) fi end: a:= n-> add(b(ithprime(n) mod m, n-1, m, m-1), 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 *)

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