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

1,3

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