%I #7 Sep 10 2017 14:53:56

%S 1,8,12,19,23,142,38,53,25,259,80,265,107,412,412,169,173,265,212,418,

%T 672,826,302,619,40,1087,63,607,467,5080,530,593,1384,1717,1384,1117,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A291758/b291758.txt">Table of n, a(n) for n = 1..16385</a>

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

%o (PARI)

%o 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

%o A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));

%o A291758(n) = (1/2)*(2 + ((A046523(n)+A048250(n))^2) - A046523(n) - 3*A048250(n));

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 10 2017