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A286571 Compound filter (prime signature of n & n/gcd(n, sigma(n))): a(n) = P(A046523(n), A017666(n)), where P(n,k) is sequence A000027 used as a pairing function. 2
1, 5, 8, 25, 17, 21, 30, 113, 70, 51, 68, 103, 93, 72, 51, 481, 155, 148, 192, 222, 331, 126, 278, 324, 382, 159, 569, 78, 437, 591, 498, 1985, 126, 237, 786, 2521, 705, 282, 952, 375, 863, 660, 948, 243, 337, 384, 1130, 1759, 1330, 1842, 237, 678, 1433, 520, 1776, 459, 1897, 567, 1772, 2076, 1893, 636, 2713, 8065, 2421, 810, 2280, 1002, 384, 2046 (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 + ((A046523(n)+A017666(n))^2) - A046523(n) - 3*A017666(n)).

PROG

(PARI)

A017666(n) = (n/gcd(n, sigma(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

A286571(n) = (1/2)*(2 + ((A046523(n)+A017666(n))^2) - A046523(n) - 3*A017666(n));

(Scheme) (define (A286571 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A017666 n)) 2) (- (A046523 n)) (- (* 3 (A017666 n))) 2)))

(Python)

from sympy import factorint, gcd, 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 a(n): return T(a046523(n), n/gcd(n, divisor_sigma(n))) # Indranil Ghosh, May 26 2017

CROSSREFS

Cf. A000027, A017666, A046523, A286360, A286570.

Sequence in context: A272577 A140113 A166652 * A234334 A025623 A069959

Adjacent sequences:  A286568 A286569 A286570 * A286572 A286573 A286574

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 26 2017

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)