A286592 -id:A286592 - cp's OEIS frontend

A286593 Compound filter (the length of rightmost run of 1's in base-2 & deficiency/abundance): a(n) = P(A089309(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 1, 5, 1, 4, 12, 24, 1, 16, 2, 30, 38, 37, 13, 32, 1, 46, 56, 80, 79, 22, 107, 139, 138, 137, 22, 173, 18, 172, 175, 281, 1, 67, 154, 122, 211, 232, 57, 139, 254, 277, 121, 327, 8, 37, 381, 439, 408, 407, 436, 212, 11, 466, 138, 564, 598, 562, 596, 668, 784, 704, 258, 196, 1, 352, 121, 782, 22, 301, 38, 864, 821, 862, 562, 632, 47, 631, 156, 1039, 947, 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, A033879, A033880, A089309, A286449, A286592, A286595.

(define (A286593 n) (* (/ 1 2) (+ (expt (+ (A089309 n) (A286449 n)) 2) (- (A089309 n)) (- (* 3 (A286449 n))) 2)))

a(n) = (1/2)*(2 + ((A089309(n)+A286449(n))^2) - A089309(n) - 3*A286449(n)).

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.

Original entry on oeis.org

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)).

A291765 Compound filter (sum of proper divisors & prime signature): a(n) = P(A001065(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.

Original entry on oeis.org

0, 2, 2, 18, 2, 61, 2, 98, 25, 86, 2, 367, 2, 115, 100, 450, 2, 517, 2, 550, 131, 185, 2, 1747, 42, 226, 203, 769, 2, 2527, 2, 1922, 205, 320, 166, 4060, 2, 373, 248, 2678, 2, 3457, 2, 1315, 979, 491, 2, 7579, 63, 1474, 346, 1642, 2, 3982, 248, 3805, 401, 698, 2, 13969, 2, 775, 1367, 7938, 295, 5749, 2, 2404, 523, 5327, 2, 18844, 2, 1030, 1819, 2839, 295

Offset: 1

Antti Karttunen, Sep 10 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16385

Cf. A000027, A000203, A001065, A046523, A286360, A286592.

A001065(n) = (sigma(n)-n);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A291765(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n));

a(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n)).

cp's OEIS Frontend

A286593 Compound filter (the length of rightmost run of 1's in base-2 & deficiency/abundance): a(n) = P(A089309(n), A286449(n)), where P(n,k) is sequence A000027 used as a pairing function.

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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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Formula

A291765 Compound filter (sum of proper divisors & prime signature): a(n) = P(A001065(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.

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