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A291750
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Compound filter: a(n) = P(A003557(n), A048250(n)), where P(n,k) is sequence A000027 used as a pairing function.
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19
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1, 4, 7, 8, 16, 67, 29, 19, 18, 154, 67, 80, 92, 277, 277, 53, 154, 94, 191, 173, 497, 631, 277, 109, 50, 862, 75, 302, 436, 2557, 497, 169, 1129, 1432, 1129, 142, 704, 1771, 1541, 214, 862, 4561, 947, 668, 328, 2557, 1129, 179, 98, 236, 2557, 905, 1432, 199, 2557, 355, 3161, 4006, 1771, 2630, 1892, 4561, 564, 593, 3487, 10297, 2279, 1487, 4561, 10297, 2557
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OFFSET
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1,2
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COMMENTS
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A000203 (sigma(n)) is a function of this sequence, because formula
A000203(n) = A092261(n) * A295294(n)
can be rewritten as a relation:
A000203(n) = A000203(A057521(n)) * A048250(n) / A048250(A057521(n)),
where A057521(n) = A064549(A003557(n)), thus A000203(n) is a function of A003557(n) and A048250(n), the values that are packed here into a(n).
A001615 (Dedekind's psi) is a function of this sequence, because it can be written as A001615(n) = A003557(n)*A048250(n).
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = (1/2)*(2 + ((A003557(n) + A048250(n))^2) - A003557(n) - 3*A048250(n)).
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PROG
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(PARI)
A003557(n) = n/factorback(factor(n)[, 1]); \\ This function from Charles R Greathouse IV, Nov 17 2014
A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
A291750(n) = (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n));
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CROSSREFS
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Cf. A000027, A000203, A001615, A003557, A048250, A291751 (rgs-version of this filter).
Sequence in context: A344581 A270216 A237599 * A007285 A225430 A295325
Adjacent sequences: A291747 A291748 A291749 * A291751 A291752 A291753
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Sep 04 2017
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STATUS
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approved
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