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A303337
Number of rectangles with semiprime area and dimensions (p) X (p+q) such that n = p+q, p < q.
2
0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 3, 0, 3, 1, 1, 0, 4, 0, 4, 0, 1, 1, 5, 0, 1, 1, 0, 0, 6, 0, 6, 0, 1, 1, 1, 0, 7, 1, 1, 0, 8, 0, 8, 0, 0, 1, 9, 0, 1, 0, 1, 0, 9, 0, 1, 0, 1, 1, 10, 0, 10, 1, 0, 0, 1, 0, 11, 0, 1, 0, 11, 0, 11, 1, 0, 0, 1, 0, 12, 0, 0, 1, 13, 0
OFFSET
1,7
COMMENTS
From Robert Israel, Jul 30 2020: (Start)
If n is prime, a(n) = A000720(floor(n/2)).
If n is a semiprime, a(n) = 1.
Otherwise a(n) = 0. (End)
FORMULA
a(n) = Sum_{i=1..floor((n-1)/2)} [Omega(n*i) = 2], where [] is the Iverson bracket and Omega = A001222.
MAPLE
f:= proc(n) if isprime(n) then numtheory:-pi(floor(n/2)) elif numtheory:-bigomega(n)=2 then 1 else 0 fi end proc:
map(f, [$1..100]); # Robert Israel, Jul 30 2020
MATHEMATICA
Table[Sum[KroneckerDelta[PrimeOmega[n*i], 2], {i, Floor[(n - 1)/2]}], {n, 100}]
PROG
(PARI) a(n) = sum(i=1, (n-1)\2, bigomega(n*i) == 2); \\ Michel Marcus, Apr 22 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 21 2018
STATUS
approved