1,4

a(n) = #{ m | A072700(m)=n};

a(n) < A066571(n).

Reinhard Zumkeller, Representing integers as arithmetic means of primes

a(6)=4, as 6 = (5+7)/2 = (2+3+13)/3 = (2+5+11)/3 = (2+3+5+7+13)/5;

a(7)=5, as 7 = 7/1 = (3+11)/2 = (3+5+13)/3 = (3+7+11)/3 = (3+5+7+13)/4.

sp:= proc(i) option remember; `if` (i=1, 2, sp(i-1) +ithprime(i)) end: b:= proc(n, i, t) if n<0 then 0 elif n=0 then `if` (t=0, 1, 0) elif i=2 then `if` (n=2 and t=1, 1, 0) else b(n, i, t):= b(n, prevprime(i), t) +b(n-i, prevprime(i), t-1) fi end: a:= proc(n) local s, k; s:= `if` (isprime(n), 1, 0); for k from 2 while sp(k)/k<=n do s:= s +b(k*n, nextprime (k*n -sp(k-1)-1), k) od; s end: seq (a(n), n=1..28); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 20 2009]

Needs["DiscreteMath`Combinatorica`"]; a = Drop[ Sort[ Subsets[ Table[ Prime[i], {i, 1, 20}]]], 1]; b = {}; Do[c = Apply[Plus, a[[n]]]/Length[a[[n]]]; If[ IntegerQ[c], b = Append[b, c]], {n, 1, 2^20 - 1}]; b = Sort[b]; Table[ Count[b, n], {n, 1, 20}]

t = Table[0, {200}]; k = 2; lst = Prime@Range@25; While[k < 2^25+1, slst = Flatten@Subsets[lst, All, {k}]; If[Mod[Plus @@ slst, Length@slst] == 0, t[[(Plus @@ slst)/(Length@slst)]]++ ]; k++ ]; t (* Robert G. Wilson v *)

Cf. A072700, A072697, A072820, A072821.

Sequence in context: A072620 A072619 A161657 this_sequence A037473 A007092 A047596

Adjacent sequences: A072698 A072699 A072700 this_sequence A072702 A072703 A072704

nonn

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 04 2002 and Jul 15 2002.

Corrected by John Layman, Jul 11, 2002

More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 20 2009