|
|
A303206
|
|
Number of partitions of n into two prime parts (p,q) such that |q-p| is squarefree.
|
|
0
|
|
|
0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 1, 0, 0, 3, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 4, 0, 0, 1, 2, 0, 0, 1, 2, 1, 0, 0, 5, 0, 0, 0, 3, 0, 0, 1, 1, 0, 0, 0, 6, 1, 0, 1, 3, 0, 0, 0, 1, 1, 0, 0, 5, 1, 0, 1, 4, 0, 0, 0, 3, 1, 0, 0, 7, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,16
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
Table[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]) MoebiusMu[n - 2 i]^2, {i, Floor[(n - 1)/2]}], {n, 100}]
Table[Count[IntegerPartitions[n, {2}], _?(AllTrue[#, PrimeQ]&&SquareFreeQ[#[[1]]-#[[2]]]&)], {n, 100}] (* Harvey P. Dale, Aug 05 2023 *)
|
|
PROG
|
(PARI) a(n) = sum(i=1, (n-1)\2, isprime(i)*isprime(n-i)*issquarefree(n-2*i)); \\ Michel Marcus, Apr 21 2018; corrected by Jun 14 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|