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A286154 Compound filter: a(n) = T(A055396(n), A000010(n)), where T(n,k) is sequence A000027 used as a pairing function. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

MathWorld, Pairing Function

FORMULA

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

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 *)

PROG

(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)));

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

(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

CROSSREFS

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

Sequence in context: A087958 A286161 A286252 * A304635 A306198 A276533

Adjacent sequences:  A286151 A286152 A286153 * A286155 A286156 A286157

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 04 2017

STATUS

approved

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Last modified September 15 20:11 EDT 2019. Contains 327086 sequences. (Running on oeis4.)