A291758 Compound filter (prime signature of n & sum of squarefree divisors of n): a(n) = P(A046523(n), A048250(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 8, 12, 19, 23, 142, 38, 53, 25, 259, 80, 265, 107, 412, 412, 169, 173, 265, 212, 418, 672, 826, 302, 619, 40, 1087, 63, 607, 467, 5080, 530, 593, 1384, 1717, 1384, 1117, 743, 2086, 1836, 844, 905, 7780, 992, 1093, 607, 2932, 1178, 1759, 59, 418, 2932, 1390, 1487, 619, 2932, 1105, 3576, 4471, 1832, 8575, 1955, 5056, 915, 2209, 3922, 14908, 2348, 2092, 5056

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, A046523, A048250, A291750, A291752, A291757.

Programs

PARI

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
A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
A291758(n) = (1/2)*(2 + ((A046523(n)+A048250(n))^2) - A046523(n) - 3*A048250(n));

Formula

a(n) = (1/2)*(2 + ((A046523(n)+A048250(n))^2) - A046523(n) - 3*A048250(n)).