A286164 - OEIS

A286164

Compound filter: a(n) = T(A055396(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function.

0, 2, 5, 7, 9, 16, 14, 29, 12, 16, 20, 67, 27, 16, 23, 121, 35, 67, 44, 67, 23, 16, 54, 277, 18, 16, 38, 67, 65, 436, 77, 497, 23, 16, 31, 631, 90, 16, 23, 277, 104, 436, 119, 67, 80, 16, 135, 1129, 25, 67, 23, 67, 152, 277, 31, 277, 23, 16, 170, 1771, 189, 16, 80, 2017, 31, 436, 209, 67, 23, 436, 230, 2557, 252, 16, 80, 67, 40, 436, 275, 1129, 138, 16, 299

(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 + ((A055396(n)+A046523(n))^2) - A055396(n) - 3*A046523(n)).

PROG

(PARI)

A001511(n) = (1+valuation(n, 2));

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

A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from Charles R Greathouse IV, Apr 23 2015

A286164(n) = (2 + ((A055396(n)+A046523(n))^2) - A055396(n) - 3*A046523(n))/2;

for(n=1, 10000, write("b286164.txt", n, " ", A286164(n)));

(Scheme) (define (A286164 n) (* (/ 1 2) (+ (expt (+ (A055396 n) (A046523 n)) 2) (- (A055396 n)) (- (* 3 (A046523 n))) 2)))

(Python)

from sympy import primepi, isprime, primefactors, factorint

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 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 a(n): return T(a055396(n), a046523(n)) # Indranil Ghosh, May 05 2017

CROSSREFS

Cf. A000027, A046523, A055396, A286160, A286161, A286162, A286163.

Sequence in context: A253275 A093417 A286162 * A211167 A083272 A115906

Adjacent sequences: A286161 A286162 A286163 * A286165 A286166 A286167

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 04 2017

STATUS

approved