OFFSET
1,36
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Sums
FORMULA
G.f.: Sum_{i>=1} Sum_{j>=i+1} Product_{k=i..j} x^prime(k). - Emeric Deutsch, Mar 30 2006
EXAMPLE
a(36)=2 because we have 36 = 17 + 19 = 5 + 7 + 11 + 13.
MAPLE
g:=sum(sum(product(x^ithprime(k), k=i..j), j=i+1..25), i=1..25): gser:=series(g, x=0, 80): seq(coeff(gser, x, n), n=1..75); # Emeric Deutsch, Mar 30 2006
# alternative, R. J. Mathar, Aug 19 2020
A084143 := proc(n::integer)
local a, k, i, spr ;
a := 0 ;
for k from 2 do
if add(ithprime(i), i=1..k) > n then
break;
end if;
for i from 1 do
spr := add( ithprime(j), j=i..i+k-1) ;
if spr > n then
break;
end if;
if spr = n then
a := a +1 ;
end if;
end do:
end do:
a ;
end proc:
MATHEMATICA
max = 25; gf = Sum[ Sum[ Product[ x^Prime[k], {k, i, j}], {j, i+1, max}], {i, 1, max}]; Rest[ CoefficientList[gf, x]][[1 ;; 75]] (* Jean-François Alcover, Oct 23 2012, after Emeric Deutsch *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, May 15 2003
STATUS
approved