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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. 2
1, 1, 8, 3, 14, 8, 42, 10, 21, 14, 76, 19, 90, 42, 63, 36, 152, 21, 208, 44, 148, 76, 322, 53, 210, 90, 228, 117, 434, 63, 625, 136, 296, 152, 402, 78, 702, 208, 375, 152, 860, 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 (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 + ((A000010(n)+A286357(n))^2) - A000010(n) - 3*A286357(n)).

PROG

(PARI)

A000010(n) = eulerphi(n);

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

A286357(n) = A001511(sigma(n));

A286568(n) = (1/2)*(2 + ((A000010(n)+A286357(n))^2) - A000010(n) - 3*A286357(n));

(Scheme) (define (A286568 n) (* (/ 1 2) (+ (expt (+ (A000010 n) (A286357 n)) 2) (- (A000010 n)) (- (* 3 (A286357 n))) 2)))

(Python)

from sympy import divisor_sigma as D, totient

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

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

def a286357(n): return a001511(D(n))

def a(n): return T(totient(n), a286357(n)) # Indranil Ghosh, May 26 2017

CROSSREFS

Cf. A000010, A000027, A286154, A286160, A286357, A286451, A286572.

Sequence in context: A069218 A248295 A265236 * A070608 A070486 A195161

Adjacent sequences:  A286565 A286566 A286567 * A286569 A286570 A286571

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 26 2017

STATUS

approved

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Last modified May 26 15:13 EDT 2019. Contains 323596 sequences. (Running on oeis4.)