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.

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

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, A000203, A053574, A286360, A286460, A286568.

Programs

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));

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

Scheme

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

Formula

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