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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
OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 26 2017
STATUS
approved