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A059339
a(n) is the number of representations of n as a sum x+y, such that bigomega(n) = bigomega(x)+bigomega(y) and 1 <= x <= y < n.
2
0, 0, 1, 1, 0, 1, 0, 1, 1, 3, 0, 2, 0, 2, 2, 1, 0, 1, 0, 2, 1, 4, 0, 2, 1, 4, 5, 6, 0, 1, 0, 2, 1, 5, 1, 3, 0, 2, 2, 4, 0, 3, 0, 5, 7, 4, 0, 3, 1, 4, 0, 7, 0, 3, 1, 5, 0, 5, 0, 6, 0, 3, 7, 4, 0, 4, 0, 10, 1, 6, 0, 4, 0, 5, 8, 10, 0, 5, 0, 6, 13, 5, 0, 7, 1, 6, 1, 8, 0, 6, 1, 11, 0, 6, 1, 7, 0, 13, 10, 11, 0
OFFSET
1,10
COMMENTS
A+B=C for 0<=A, 0<=B, A<=B; if n is a C-almost prime then a(n) = number of decompositions of n into sum of an A-almost prime and a B-almost prime. - The original definition of the sequence.
LINKS
EXAMPLE
For n=10, bigomega(10) = 2 [where bigomega = A001222]. There are three solutions: 10 = 1+9 (with bigomega(1) = 0 and bigomega(9) = 2) = 7+3 (with bigomega(7) = bigomega(3) = 1) = 5+5 (with bigomega(5) = 1), thus a(10) = 3. - Antti Karttunen, Jul 28 2024
Original example was: E.g. n=10, 10 is 2-almost prime (semiprime). Therefore C=2. 10=1+9(A=0,B=2); 10=7+3(A=1,B=1); 10=5+5(A=1,B=1), so a(10)=3.
PROG
(PARI) A059339(n) = { my(o=bigomega(n)); sum(i=1, n\2, (bigomega(i)+bigomega(n-i))==o); }; \\ Antti Karttunen, Jul 19 2024
CROSSREFS
Cf. A001222, A374210 (partial sums).
Sequence in context: A161970 A230446 A260737 * A241181 A171772 A092735
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Jan 27 2001
EXTENSIONS
New name added and the old definition moved to the comments by Antti Karttunen, Jul 20 2024
STATUS
approved