The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A286164

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A286164

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

#12 by N. J. A. Sloane at Wed May 10 21:37:38 EDT 2017

STATUS

proposed

approved

#11 by Indranil Ghosh at Wed May 10 14:03:23 EDT 2017

STATUS

editing

proposed

#10 by Indranil Ghosh at Wed May 10 14:03:11 EDT 2017

PROG

def P(n):

f = factorint(n)

def P(n): return sorted([factorint(n)f[i] for i in factorint(n)f])

STATUS

approved

editing

#9 by N. J. A. Sloane at Sat May 06 00:00:09 EDT 2017

STATUS

proposed

approved

#8 by Indranil Ghosh at Fri May 05 13:17:09 EDT 2017

STATUS

editing

proposed

#7 by Indranil Ghosh at Fri May 05 13:16:35 EDT 2017

PROG

(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): return sorted([factorint(n)[i] for i in factorint(n)])

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

STATUS

approved

editing

#6 by N. J. A. Sloane at Thu May 04 09:40:49 EDT 2017

STATUS

proposed

approved

#5 by Antti Karttunen at Thu May 04 09:38:29 EDT 2017

STATUS

editing

proposed

#4 by Antti Karttunen at Thu May 04 09:33:12 EDT 2017

NAME

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

Discussion

Thu May 04

09:38

Antti Karttunen: Used as a filtering sequence, thus longish data section.

#3 by Antti Karttunen at Thu May 04 09:30:00 EDT 2017

LINKS

Antti Karttunen, <a href="/A286164/b286164.txt">Table of n, a(n) for n = 1..10000</a>

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)));