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

Author

Antti Karttunen, Sep 04 2017

Keywords

• nonn

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

Crossrefs

Cf. A000027, A000203, A001615, A003557, A048250, A291751 (rgs-version of this filter).

Programs

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));

Formula

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