A291750 Compound filter: a(n) = P(A003557(n), A048250(n)), where P(n,k) is sequence A000027 used as a pairing function.

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

Offset

1,2

Comments

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).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = (1/2)*(2 + ((A003557(n) + A048250(n))^2) - A003557(n) - 3*A048250(n)).

Prog

(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));

Crossrefs

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

Keyword

nonn

Author

Antti Karttunen, Sep 04 2017

Status

approved