A286154 Compound filter: a(n) = T(A055396(n), A000010(n)), where T(n,k) is sequence A000027 used as a pairing function.

0, 1, 5, 2, 18, 2, 40, 7, 23, 7, 96, 7, 142, 16, 38, 29, 238, 16, 308, 29, 80, 46, 444, 29, 234, 67, 173, 67, 676, 29, 791, 121, 212, 121, 328, 67, 1093, 154, 302, 121, 1339, 67, 1499, 191, 302, 232, 1785, 121, 994, 191, 530, 277, 2227, 154, 864, 277, 668, 379, 2718, 121, 2944, 436, 668, 497, 1228, 191, 3505, 497, 992, 277, 3936, 277, 4207, 631, 822, 631

Offset: 1

Author

Antti Karttunen, May 04 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• MathWorld, Pairing Function

Crossrefs

Cf. A000010, A000027, A055396, A286142, A286143, A286144, A286152, A286160, A286161, A286162, A286163, A286164.

Programs

Mathematica

Table[(2 + (#1 + #2)^2 - #1 - 3 #2)/2 & @@ {If[n == 1, 0, PrimePi[ FactorInteger[n][[1, 1]] ]], EulerPhi@ n}, {n, 76}] (* Michael De Vlieger, May 04 2017 *)

PARI

A000010(n) = eulerphi(n);
A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from Charles R Greathouse IV, Apr 23 2015
A286154(n) = (2 + ((A055396(n)+A000010(n))^2) - A055396(n) - 3*A000010(n))/2;
for(n=1, 10000, write("b286154.txt", n, " ", A286154(n)));

Python

from sympy import primepi, isprime, primefactors, totient
def a049084(n): return primepi(n)*(1*isprime(n))
def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a(n): return T(a055396(n), totient(n)) # Indranil Ghosh, May 05 2017

Scheme

(define (A286154 n) (* (/ 1 2) (+ (expt (+ (A055396 n) (A000010 n)) 2) (- (A055396 n)) (- (* 3 (A000010 n))) 2)))

Formula

a(n) = (1/2)*(2 + ((A055396(n)+A000010(n))^2) - A055396(n) - 3*A000010(n)).