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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 10 15:09 EST 2019. Contains 329896 sequences. (Running on oeis4.)