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A286144 Compound filter: a(n) = T(A000010(n), A257993(n)), where T(n,k) is sequence A000027 used as a pairing function. 7
1, 2, 3, 5, 10, 8, 21, 14, 21, 14, 55, 19, 78, 27, 36, 44, 136, 34, 171, 44, 78, 65, 253, 53, 210, 90, 171, 90, 406, 63, 465, 152, 210, 152, 300, 103, 666, 189, 300, 152, 820, 103, 903, 230, 300, 275, 1081, 169, 903, 230, 528, 324, 1378, 208, 820, 324, 666, 434, 1711, 187, 1830, 495, 666, 560, 1176, 251, 2211, 560, 990, 324, 2485, 349, 2628, 702, 820, 702 (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 + ((A000010(n)+A257993(n))^2) - A000010(n) - 3*A257993(n)).

MATHEMATICA

Table[(2 + (#1 + #2)^2 - #1 - 3 #2)/2 & @@ {EulerPhi@ n, Module[{i = 1}, While[! CoprimeQ[Prime@ i, n], i++]; i]}, {n, 74}] (* Michael De Vlieger, May 04 2017 *)

PROG

(PARI)

A000010(n) = eulerphi(n);

A257993(n) = { for(i=1, n, if(n%prime(i), return(i))); }

A286144(n) = (2 + ((A000010(n)+A257993(n))^2) - A000010(n) - 3*A257993(n))/2;

for(n=1, 10000, write("b286144.txt", n, " ", A286144(n)));

(Scheme) (define (A286144 n) (* (/ 1 2) (+ (expt (+ (A000010 n) (A257993 n)) 2) (- (A000010 n)) (- (* 3 (A257993 n))) 2)))

(Python)

from sympy import prime, primepi, gcd, totient

def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

def a053669(n):

    x=1

    while True:

        if gcd(prime(x), n) == 1: return prime(x)

        else: x+=1

def a257993(n): return primepi(a053669(n))

def a(n): return T(totient(n), a257993(n)) # Indranil Ghosh, May 05 2017

CROSSREFS

Cf. A000010, A000027, A257993, A286142, A286143, A286152, A286160, A286161, A286162, A286163, A286164.

Sequence in context: A250747 A241262 A244489 * A038807 A094542 A175481

Adjacent sequences:  A286141 A286142 A286143 * A286145 A286146 A286147

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 04 2017

STATUS

approved

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)