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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
1, 8, 7, 39, 16, 80, 29, 157, 79, 173, 67, 438, 92, 302, 277, 600, 154, 782, 191, 949, 497, 668, 277, 1957, 466, 905, 781, 1656, 436, 2630, 497, 2284, 1129, 1487, 1129, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Pairing Function

Index entries for sequences related to sigma(n)

FORMULA

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

PROG

(PARI)

A000203(n) = sigma(n);

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

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

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

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

(Python)

from sympy import divisor_sigma as D

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

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

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

print [a(n) for n in xrange(1, 101)] # Indranil Ghosh, May 12 2017

CROSSREFS

Cf. A000027, A286360.

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

Sequence in context: A267093 A090099 A138809 * A317231 A237646 A288188

Adjacent sequences:  A286457 A286458 A286459 * A286461 A286462 A286463

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 10 2017

STATUS

approved

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Last modified May 19 02:45 EDT 2019. Contains 323377 sequences. (Running on oeis4.)