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.

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

Offset: 1

Author

Antti Karttunen, May 26 2017

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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));

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

Scheme

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

Formula

a(n) = (1/2)*(2 + ((A000010(n)+A286357(n))^2) - A000010(n) - 3*A286357(n)).