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A286573 Compound filter: a(n) = P(A007733(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function. 6
1, 2, 5, 7, 14, 23, 9, 29, 42, 40, 65, 80, 90, 31, 40, 121, 44, 142, 189, 109, 61, 115, 77, 302, 273, 148, 318, 94, 434, 532, 20, 497, 115, 86, 148, 826, 702, 271, 148, 355, 230, 601, 119, 220, 265, 131, 299, 1178, 297, 485, 86, 265, 1430, 838, 320, 328, 271, 556, 1769, 1957, 1890, 50, 142, 2017, 148, 751, 2277, 179, 373, 832, 665, 2932, 54, 856, 485 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

a(n) = (1/2)*(2 + ((A007733(n)+A046523(n))^2) - A007733(n) - 3*A046523(n)).

PROG

(PARI)

A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ This function from Michel Marcus, Apr 11 2015

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

A286573(n) = (1/2)*(2 + ((A007733(n)+A046523(n))^2) - A007733(n) - 3*A046523(n));

(Python)

from sympy import divisors, factorint

def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

def a002326(n):

    m=1

    while True:

        if (2**m - 1)%(2*n + 1)==0: return m

        else: m+=1

def a000265(n): return max(list(filter(lambda i: i%2 == 1, divisors(n))))

def a007733(n): return a002326((a000265(n) - 1)/2)

def P(n):

    f = factorint(n)

    return sorted([f[i] for i in f])

def a046523(n):

    x=1

    while True:

        if P(n) == P(x): return x

        else: x+=1

def a(n): return T(a007733(n), a046523(n)) # Indranil Ghosh, May 26 2017

CROSSREFS

Cf. A000027, A007733, A046523, A286160, A286161.

Sequence in context: A132603 A022765 A228208 * A133511 A257025 A076720

Adjacent sequences:  A286570 A286571 A286572 * A286574 A286575 A286576

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 26 2017

STATUS

approved

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Last modified May 26 15:15 EDT 2019. Contains 323596 sequences. (Running on oeis4.)