A286149 - OEIS

A286149

Compound filter: a(n) = T(A046523(n), A109395(n)), where T(n,k) is sequence A000027 used as a pairing function.

1, 5, 8, 14, 17, 34, 30, 44, 19, 51, 68, 103, 93, 72, 196, 152, 155, 103, 192, 132, 72, 126, 278, 349, 32, 159, 53, 165, 437, 976, 498, 560, 709, 237, 786, 739, 705, 282, 159, 402, 863, 660, 948, 243, 337, 384, 1130, 1273, 49, 132, 1546, 288, 1433, 349, 126, 459, 282, 567, 1772, 2761, 1893, 636, 165, 2144, 2421, 1921, 2280, 390, 2707, 2046, 2558, 2773, 2703

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

MathWorld, Pairing Function

FORMULA

a(n) = (1/2)*(2 + ((A046523(n)+A109395(n))^2) - A046523(n) - 3*A109395(n)).

MATHEMATICA

Table[(2 + (#1 + #2)^2 - #1 - 3 #2)/2 & @@ {Times @@ MapIndexed[ Prime[First@ #2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]] - Boole[n == 1], Denominator[EulerPhi[n]/n]}, {n, 73}] (* Michael De Vlieger, May 04 2017 *)

PROG

(PARI)

A109395(n) = n/gcd(n, eulerphi(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

A286149(n) = (1/2)*(2 + ((A046523(n)+A109395(n))^2) - A046523(n) - 3*A109395(n));

for(n=1, 10000, write("b286149.txt", n, " ", A286149(n)));

(Scheme) (define (A286149 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A109395 n)) 2) (- (A046523 n)) (- (* 3 (A109395 n))) 2)))

(Python)

from sympy import factorint, totient, gcd

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: