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A286034 Compound filter: a(n) = P(A046523(n), A161942(n)), where P(n,k) is sequence A000027 used as a pairing function. 6
1, 8, 3, 49, 8, 34, 3, 239, 124, 97, 8, 165, 30, 34, 34, 1051, 47, 1237, 17, 508, 21, 97, 8, 727, 565, 331, 74, 165, 122, 733, 3, 4403, 34, 502, 34, 7911, 192, 196, 72, 2302, 233, 526, 68, 508, 1237, 97, 8, 3051, 1774, 5368, 97, 1782, 380, 727, 97, 727, 51, 1231, 122, 3220, 498, 34, 288, 18019, 331, 733, 155, 2713, 34, 733, 47, 35317, 705, 1897, 873, 1047, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

MathWorld, Pairing Function

FORMULA

a(n) = (1/2)*(2 + ((A046523(n)+A161942(n))^2) - A046523(n) - 3*A161942(n)).

PROG

(PARI)

A000265(n) = (n >> valuation(n, 2));

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

A161942(n) = A000265(sigma(n));

A286034(n) = (2 + ((A046523(n)+A161942(n))^2) - A046523(n) - 3*A161942(n))/2;

for(n=1, 16384, write("b286034.txt", n, " ", A286034(n)));

(Scheme) (define (A286034 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A161942 n)) 2) (- (A046523 n)) (- (* 3 (A161942 n))) 2)))

(Python)

from sympy import factorint, divisors, divisor_sigma

def T(n, m): return ((n + m)**2 - n - 3*m + 2)/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 a000265(n): return max(list(filter(lambda i: i%2 == 1, divisors(n))))

def a161942(n): return a000265(divisor_sigma(n))

def a(n): return T(a046523(n), a161942(n)) # Indranil Ghosh, May 07 2017

CROSSREFS

Cf. A000027, A046523, A161942, A286260.

Sequence in context: A182054 A302214 A049074 * A256046 A197245 A302462

Adjacent sequences:  A286031 A286032 A286033 * A286035 A286036 A286037

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 07 2017

STATUS

approved

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Last modified October 23 03:42 EDT 2021. Contains 348211 sequences. (Running on oeis4.)