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Search: id:A116852
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| A116852 |
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Number of partitions of n-th semiprime into 2 squares. |
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+0
1
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| 1, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0
(list; graph; listen)
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OFFSET
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1,9
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COMMENT
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See also A000161 Number of partitions of n into 2 squares (when order does not matter, and zero is allowed).
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FORMULA
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a(n) = A000161(A001358(n)).
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EXAMPLE
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a(1) = 1 because semiprime(1) = 4 = 0^2 + 2^2, the unique sum of squares.
a(2) = 0 because semiprime(2) = 6 has no decomposition into sum of 2 squares because it has a prime factor p == 3 (mod 4) with an odd power.
a(3) = 1 because semiprime(3) = 9 = 0^2 + 3^2, the unique sum of squares.
a(4) = 1 because semiprime(4) = 10 = 2*5 = 1^2 + 3^2.
a(9) = 2 because semiprime(9) = 25 = 0^2 + 5^2 = 3^2 + 4^2, two distinct ways.
a(23) = 2 because semiprime(23) = 65 = 5*13 = 1^2 + 8^2 = 4^2 + 7^2.
a(28) = 2 because semiprime(28) = 85 = 5*17 = 2^2 + 9^2 = 6^2 + 7^2.
a(49) = 2 because semiprime(49) = 145 = 5*29 = 1^2 + 12^2 = 8^2 + 9^2.
a(56) = 2 because semiprime(56) = 169 = 0^2 + 13^2 = 5^2 + 12^2.
a(60) = 2 because semiprime(60) = 185 = 5*37 = 4^2 + 13^2 = 8^2 + 11^2.
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CROSSREFS
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Cf. A000161, A001358.
Sequence in context: A062735 A054547 A025439 this_sequence A060154 A061007 A085252
Adjacent sequences: A116849 A116850 A116851 this_sequence A116853 A116854 A116855
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Mar 15 2006
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