A186336 Number of ways of representing n as the sum of one or more consecutive semiprimes.

0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 0, 0, 0, 2, 1, 1, 1, 0, 1, 3, 0, 0, 0, 2, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 0, 1, 3, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 3, 0, 0, 1, 2, 1, 1, 0, 2, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 1, 0, 0, 0, 3, 2, 0, 1, 0, 1, 2, 0, 0, 2, 1, 0, 2, 1, 1

Offset: 0

Author

Alois P. Heinz, Feb 18 2011

Keywords

• nonn

Examples

			a(4)  = 1:  4 = A001358(1) is the first semiprime.
a(10) = 2: 10 = A001358(1)+A001358(2) = 4+6 = A001358(4) = 10.
a(39) = 3: 39 = 6+9+10+14 = 10+14+15 = 39.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001358, A112020, A186337.

Programs

Haskell

a186336 n = f $ takeWhile (<= n) a001358_list where
   f []       = 0
   f (sp:sps) = g sp sps + f sps
   g spSum []                    = fromEnum (spSum == n)
   g spSum (sp:sps) | spSum < n  = g (sp + spSum) sps
                    | spSum == n = 1
                    | otherwise  = 0
-- Reinhard Zumkeller, Feb 28 2011

Maple

b:= proc(n) option remember; local k;
      if n=0 then 0
    else for k from b(n-1)+1
           while isprime(k) or 2<>add(i[2], i=ifactors(k)[2])
         do od; k
      fi
    end:
pis:= proc(n) option remember; local k;
        if n<4 then 0
      elif n=4 then 1
      else k:= pis(n-1);
           k +`if`(b(k+1)=n, 1 ,0)
        fi
      end:
ssp:= proc(i,j) option remember;
        b(j) + `if`(i=j, 0, ssp(i, j-1))
      end:
a:= proc(n) option remember; local i, j, cnt, s;
      cnt:= 0;
      j:= pis(n);
      i:= j;
      while i>0 do
        s:= ssp(i,j);
        if sn then j:= j-1
      else cnt:= cnt+1;
           i, j:= i-1, j-1
        fi
      od; cnt
    end:
seq(a(n), n=0..200);

Mathematica

nmax = 120;
sp = Select[Range[nmax], PrimeOmega[#] == 2&];
lsp = Length[sp]; Clear[a]; a[_] = 0;
Do[n = Total[sp[[i ;; j]]]; a[n] = a[n]+1, {i, 1, lsp}, {j, i, lsp}];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Mar 13 2019 *)