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A286570 Compound filter (prime signature of n & gcd(n, sigma(n))): a(n) = P(A046523(n), A009194(n)), where P(n,k) is sequence A000027 used as a pairing function. 4
1, 3, 3, 10, 3, 61, 3, 36, 10, 27, 3, 117, 3, 27, 34, 136, 3, 103, 3, 90, 21, 27, 3, 619, 10, 27, 36, 753, 3, 625, 3, 528, 34, 27, 21, 666, 3, 27, 21, 552, 3, 625, 3, 117, 103, 27, 3, 1323, 10, 78, 34, 90, 3, 430, 21, 489, 21, 27, 3, 2545, 3, 27, 78, 2080, 21, 625, 3, 90, 34, 495, 3, 2773, 3, 27, 78, 117, 21, 625, 3, 1224, 136, 27, 3, 3801, 21, 27, 34, 375, 3 (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)+A009194(n))^2) - A046523(n) - 3*A009194(n)).

PROG

(PARI)

A009194(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

A286570(n) = (1/2)*(2 + ((A046523(n)+A009194(n))^2) - A046523(n) - 3*A009194(n));

(Scheme) (define (A286570 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A009194 n)) 2) (- (A046523 n)) (- (* 3 (A009194 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), gcd(n, divisor_sigma(n))) # Indranil Ghosh, May 26 2017

CROSSREFS

Cf. A000027, A009194, A046523, A286360, A286571, A286591.

Sequence in context: A072004 A095271 A054511 * A134704 A057210 A278832

Adjacent sequences:  A286567 A286568 A286569 * A286571 A286572 A286573

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 26 2017

STATUS

approved

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Last modified May 26 19:24 EDT 2019. Contains 323597 sequences. (Running on oeis4.)