A291765 Compound filter (sum of proper divisors & prime signature): a(n) = P(A001065(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.

0, 2, 2, 18, 2, 61, 2, 98, 25, 86, 2, 367, 2, 115, 100, 450, 2, 517, 2, 550, 131, 185, 2, 1747, 42, 226, 203, 769, 2, 2527, 2, 1922, 205, 320, 166, 4060, 2, 373, 248, 2678, 2, 3457, 2, 1315, 979, 491, 2, 7579, 63, 1474, 346, 1642, 2, 3982, 248, 3805, 401, 698, 2, 13969, 2, 775, 1367, 7938, 295, 5749, 2, 2404, 523, 5327, 2, 18844, 2, 1030, 1819, 2839, 295

Offset: 1

Author

Antti Karttunen, Sep 10 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16385

Crossrefs

Cf. A000027, A000203, A001065, A046523, A286360, A286592.

Programs

PARI

A001065(n) = (sigma(n)-n);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A291765(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n));

Formula

a(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n)).