A286451 -id:A286451 - cp's OEIS frontend

A286595 Compound filter (2-adic valuation & deficiency/abundance): a(n) = P(A001511(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 3, 2, 6, 4, 12, 11, 10, 16, 5, 22, 48, 37, 8, 11, 15, 46, 68, 67, 108, 22, 107, 106, 175, 137, 30, 154, 18, 172, 138, 191, 21, 67, 173, 106, 256, 232, 57, 106, 329, 277, 138, 301, 13, 37, 353, 352, 501, 407, 467, 191, 24, 466, 138, 497, 634, 562, 632, 631, 744, 704, 192, 106, 28, 352, 138, 742, 39, 301, 38, 781, 950, 862, 597, 596, 58, 631, 138, 904, 1133, 407

Offset: 1

Antti Karttunen, May 21 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A000027, A001511, A033879, A033880, A286449, A286260, A286451, A286460, A286592, A286593.

(define (A286595 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A286449 n)) 2) (- (A001511 n)) (- (* 3 (A286449 n))) 2)))

a(n) = (1/2)*(2 + ((A001511(n)+A286449(n))^2) - A001511(n) - 3*A286449(n)).

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.

Original entry on oeis.org

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

Antti Karttunen, May 26 2017

nonn

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

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

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));

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

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

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

cp's OEIS Frontend

A286595 Compound filter (2-adic valuation & deficiency/abundance): a(n) = P(A001511(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.

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