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

1,3

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, 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 *)

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