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A286568 Compound filter (phi(n) & 2-adic valuation of sigma(n)): a(n) = P(A000010(n), A286357(n)), where P(n,k) is sequence A000027 used as a pairing function.

%I A286568 #10 May 26 2017 16:38:06
%S A286568 1,1,8,3,14,8,42,10,21,14,76,19,90,42,63,36,152,21,208,44,148,76,322,
%T A286568 53,210,90,228,117,434,63,625,136,296,152,402,78,702,208,375,152,860,
%U A286568 148,988,251,324,322,1271,169,903,210,627,324,1430,228,943,375,816,434,1828,187,1890,625,777,528,1273,296,2344,560,1220,402,2698,300,2700,702,901
%N A286568 Compound filter (phi(n) & 2-adic valuation of sigma(n)): a(n) = P(A000010(n), A286357(n)), where P(n,k) is sequence A000027 used as a pairing function.
%H A286568 Antti Karttunen, <a href="/A286568/b286568.txt">Table of n, a(n) for n = 1..10000</a>
%F A286568 a(n) = (1/2)*(2 + ((A000010(n)+A286357(n))^2) - A000010(n) - 3*A286357(n)).
%o A286568 (PARI)
%o A286568 A000010(n) = eulerphi(n);
%o A286568 A001511(n) = (1+valuation(n,2));
%o A286568 A286357(n) = A001511(sigma(n));
%o A286568 A286568(n) = (1/2)*(2 + ((A000010(n)+A286357(n))^2) - A000010(n) - 3*A286357(n));
%o A286568 (Scheme) (define (A286568 n) (* (/ 1 2) (+ (expt (+ (A000010 n) (A286357 n)) 2) (- (A000010 n)) (- (* 3 (A286357 n))) 2)))
%o A286568 (Python)
%o A286568 from sympy import divisor_sigma as D, totient
%o A286568 def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
%o A286568 def a001511(n): return bin(n)[2:][::-1].index("1") + 1
%o A286568 def a286357(n): return a001511(D(n))
%o A286568 def a(n): return T(totient(n), a286357(n)) # _Indranil Ghosh_, May 26 2017
%Y A286568 Cf. A000010, A000027, A286154, A286160, A286357, A286451, A286572.
%K A286568 nonn
%O A286568 1,3
%A A286568 _Antti Karttunen_, May 26 2017