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

1,3

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