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

1,2

Links

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

Formula

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

Prog

(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));

Crossrefs

Cf. A000027, A046523, A048250, A291750, A291752, A291757.

Sequence in context: A033477 A105936 A168670 * A232867 A358574 A084488

Adjacent sequences: A291755 A291756 A291757 * A291759 A291760 A291761

Keyword

nonn

Author

Antti Karttunen, Sep 10 2017

Status

approved