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A286460 Compound filter (2-adic valuation & sum of the divisors): a(n) = P(A001511(n), A000203(n)), where P(n,k) is sequence A000027 used as a pairing function. 7

%I

%S 1,8,7,39,16,80,29,157,79,173,67,438,92,302,277,600,154,782,191,949,

%T 497,668,277,1957,466,905,781,1656,436,2630,497,2284,1129,1487,1129,

%U 4281,704,1832,1541,4282,862,4658,947,3658,3004,2630,1129,8133,1597,4373,2557,4953,1432,7262,2557,7507,3161,4097,1771,14368,1892,4658,5357,8785,3487,10442,2279

%N Compound filter (2-adic valuation & sum of the divisors): a(n) = P(A001511(n), A000203(n)), where P(n,k) is sequence A000027 used as a pairing function.

%H Antti Karttunen, <a href="/A286460/b286460.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = (1/2)*(2 + ((A001511(n)+A000203(n))^2) - A001511(n) - 3*A000203(n)).

%o (PARI)

%o A000203(n) = sigma(n);

%o A001511(n) = (1+valuation(n,2));

%o A286460(n) = (1/2)*(2 + ((A001511(n)+A000203(n))^2) - A001511(n) - 3*A000203(n));

%o for(n=1, 10000, write("b286460.txt", n, " ", A286460(n)));

%o (Scheme) (define (A286460 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A000203 n)) 2) (- (A001511 n)) (- (* 3 (A000203 n))) 2)))

%o (Python)

%o from sympy import divisor_sigma as D

%o def a001511(n): return bin(n)[2:][::-1].index("1") + 1

%o def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

%o def a(n): return T(a001511(n), D(n))

%o print [a(n) for n in range(1, 101)] # _Indranil Ghosh_, May 12 2017

%Y Cf. A000027, A286360.

%Y Cf. A000593, A146076 (sequences matching to this filter), also A000203, A161942, A286260, A286357.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 10 2017

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Last modified April 16 17:01 EDT 2021. Contains 343050 sequences. (Running on oeis4.)