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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.

%I A291765 #6 Sep 10 2017 14:54:18
%S A291765 0,2,2,18,2,61,2,98,25,86,2,367,2,115,100,450,2,517,2,550,131,185,2,
%T A291765 1747,42,226,203,769,2,2527,2,1922,205,320,166,4060,2,373,248,2678,2,
%U A291765 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
%N 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.
%H A291765 Antti Karttunen, <a href="/A291765/b291765.txt">Table of n, a(n) for n = 1..16385</a>
%F A291765 a(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n)).
%o A291765 (PARI)
%o A291765 A001065(n) = (sigma(n)-n);
%o A291765 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 A291765 A291765(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n));
%Y A291765 Cf. A000027, A000203, A001065, A046523, A286360, A286592.
%K A291765 nonn
%O A291765 1,2
%A A291765 _Antti Karttunen_, Sep 10 2017