OFFSET
0,20
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 1000 terms from Harvey P. Dale)
FORMULA
a(n) = Sum_{i=1..floor((n-1)/2)} [Omega(i) = 2] * [Omega(n-i) = 2], where Omega = A001222 and [] is the Iverson bracket.
EXAMPLE
a(19) = 2; 19 = 15+4 = 10+9.
MAPLE
h:= proc(n) option remember; `if`(n=0, 0,
`if`(numtheory[bigomega](n)=2, n, h(n-1)))
end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
`if`(i>n, 0, x*b(n-i, h(min(n-i, i-1))))+b(n, h(i-1)))), x, 3)
end:
a:= n-> coeff(b(n, h(n)), x, 2):
seq(a(n), n=0..120); # Alois P. Heinz, May 26 2021
MATHEMATICA
Table[Sum[KroneckerDelta[PrimeOmega[i], 2] KroneckerDelta[PrimeOmega[n - i], 2], {i, Floor[(n - 1)/2]}], {n, 100}]
Table[Count[IntegerPartitions[n, {2}], _?(PrimeOmega[#[[1]]]==PrimeOmega[#[[2]]]==2&&#[[1]]!=#[[2]]&)], {n, 90}] (* Harvey P. Dale, Aug 03 2020 *)
PROG
(PARI) a(n) = sum(i=1, (n-1)\2, (bigomega(i)==2)*(bigomega(n-i)==2)); \\ Michel Marcus, Apr 08 2018
CROSSREFS
KEYWORD
AUTHOR
Wesley Ivan Hurt, Apr 04 2018
STATUS
approved