A057611 Let m = 3, 5, 7, ..., k = 0, 1, 2, 3, ..., z = (m+1)/2, 0 < j <= m. Let n_j be a prime number. Sequence gives T(m,k) = Table[m,k] = number of solutions to Sum_{d=1,2, ..., (z+k)}(n_j)_d = Sum_{d=1,2, ..., (z-k-1)}(n_j)_d = primorial number (A002110).

1, 1, 0, 2, 0, 0, 5, 0, 0, 0, 8, 5, 0, 0, 0, 19, 20, 0, 0, 0, 0, 66, 55, 1, 0, 0, 0, 0, 280, 48, 64, 0, 0, 0, 0, 0, 645, 584, 35, 22, 0, 0, 0, 0, 0, 2780, 842, 705, 10, 4, 0, 0, 0, 0, 0, 9163, 2754, 2867, 30, 46, 0, 0, 0, 0, 0, 0, 29869, 10771, 9904, 311, 230, 0, 0, 0, 0, 0, 0, 0

Offset

0,4

Links

Table of n, a(n) for n=0..77.

Formula

A022894(m) = Sum_{k=0, 1, 2, ..} [Number of solutions to Sum_{d=1, 2, ..., (z+k)}(n_j)_d = Sum_{ d=1, 2, ..., (z-k-1)}(n_j)_d]

Example

{1}; {1,0}; {2,0,0}; {5,0,0,0}; {8,5,0,0,0}; {19,20,0,0,0,0}; ..... ->-> 3+2=5 {m=3, Table[3,0]=1}; 2+7+5=3+11 {m=5, Table[5,0]=1, Table[5,1]=0}; 17+2+7+3=13+5+11 and 2+11+3+13=17+7+5 {m=7, Table[7,0]=2, Table[7,1]=0, Table[7,2]=0}.

Crossrefs

Cf. A022894, A002110.

Sequence in context: A169774 A302689 A289088 * A329959 A259701 A147843

Adjacent sequences: A057608 A057609 A057610 * A057612 A057613 A057614

Keyword

nonn,tabl

Author

Naohiro Nomoto, Nov 27 2000

Status

approved