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A286572 Compound filter (2-adic valuation of phi(n) & sigma(n)): a(n) = P(A053574(n), A000203(n)), where P(n,k) is sequence A000027 used as a pairing function. 3
0, 1, 7, 22, 23, 67, 29, 122, 79, 173, 67, 408, 107, 277, 328, 531, 214, 742, 191, 949, 530, 631, 277, 1894, 498, 905, 781, 1598, 467, 2704, 497, 2149, 1178, 1600, 1228, 4188, 743, 1771, 1656, 4282, 949, 4658, 947, 3572, 3163, 2557, 1129, 8005, 1597, 4373, 2855, 4953, 1487, 7141, 2704, 7384, 3242, 4097, 1771, 14539, 1955, 4561, 5462, 8520, 3745 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

a(n) = (1/2)*(2 + ((A053574(n)+A000203(n))^2) - A053574(n) - 3*A000203(n)).

PROG

(PARI)

A000203(n) = sigma(n);

A053574(n) = valuation(eulerphi(n), 2);

A286572(n) = (1/2)*(2 + ((A053574(n)+A000203(n))^2) - A053574(n) - 3*A000203(n));

(Scheme) (define (A286572 n) (* (/ 1 2) (+ (expt (+ (A053574 n) (A000203 n)) 2) (- (A053574 n)) (- (* 3 (A000203 n))) 2)))

(Python)

from sympy import totient, divisor_sigma

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

def a007814(n): return 1 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")

def a(n): return T(a007814(totient(n)), divisor_sigma(n)) # Indranil Ghosh, May 26 2017

CROSSREFS

Cf. A000010, A000027, A000203, A053574, A286360, A286460, A286568.

Sequence in context: A217014 A200886 A070412 * A055575 A297712 A041090

Adjacent sequences:  A286569 A286570 A286571 * A286573 A286574 A286575

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 26 2017

STATUS

approved

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Last modified December 2 10:47 EST 2021. Contains 349440 sequences. (Running on oeis4.)