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(Python)

from sympy import factorint

from operator import mul

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 a061395(n): return 0 if n == 1 else primepi(max(primefactors(n)))

def a(n): return T(a061395(n), a046523(n)) # Indranil Ghosh, May 09 2017

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Antti Karttunen, <a href="/A286356/b286356.txt">Table of n, a(n) for n = 1..10000</a>

(PARI)

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

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530.

A286356(n) = (2 + ((A061395(n)+A046523(n))^2) - A061395(n) - 3*A046523(n))/2;

for(n=1, 10000, write("b286356.txt", n, " ", A286356(n)));

Compound filter: a(n) = P(A061395(n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

a(n) = (1/2)*(2 + ((A061395(n)+A046523(n))^2) - A061395(n) - 3*A046523(n)).

allocated for Antti Karttunen

Compound filter:

0, 2, 5, 7, 9, 23, 14, 29, 12, 31, 20, 80, 27, 40, 31, 121, 35, 80, 44, 94, 40, 50, 54, 302, 18, 61, 38, 109, 65, 499, 77, 497, 50, 73, 40, 668, 90, 86, 61, 328, 104, 532, 119, 125, 94, 100, 135, 1178, 25, 94, 73, 142, 152, 302, 50, 355, 86, 115, 170, 1894, 189, 131, 109, 2017, 61, 566, 209, 160, 100, 532, 230, 2630, 252, 148, 94, 179, 50, 601, 275, 1228, 138

1,2

(Scheme) (define (A286356 n) (* (/ 1 2) (+ (expt (+ (A061395 n) (A046523 n)) 2) (- (A061395 n)) (- (* 3 (A046523 n))) 2)))

Cf. A000027, A046523, A061395, A286164.

allocated

nonn

Antti Karttunen, May 09 2017

approved

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allocating

allocated

allocated for Antti Karttunen

allocating

approved