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A286250 Filter-sequence: a(n) = A278223(A064216(n)) = A046523((2*A064216(n))-1).

%I A286250 #10 May 13 2017 17:24:02
%S A286250 1,2,2,4,2,2,6,2,4,6,2,2,2,6,12,6,8,2,2,2,2,16,2,6,4,6,6,2,2,30,12,6,
%T A286250 6,4,12,6,6,6,6,6,2,2,6,6,30,2,6,2,6,6,2,6,2,6,6,6,6,2,6,6,2,12,2,36,
%U A286250 2,6,4,2,12,30,12,12,2,12,2,24,2,2,6,6,24,2,2,12,2,24,12,2,2,30,30,6,6,2,2,4,6,2,30,6,32,2,6,2,6,2,6,12,4,2,30,2,2
%N A286250 Filter-sequence: a(n) = A278223(A064216(n)) = A046523((2*A064216(n))-1).
%H A286250 Antti Karttunen, <a href="/A286250/b286250.txt">Table of n, a(n) for n = 1..10000</a>
%F A286250 a(n) = A046523(A245448(n)) = A278223(A064216(n)) = A046523((2*A064216(n))-1).
%o A286250 (PARI)
%o A286250 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
%o A286250 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A286250 A064216(n) = A064989((2*n)-1);
%o A286250 A286250(n) = A046523(-1+(2*A064216(n)));
%o A286250 for(n=1, 10000, write("b286250.txt", n, " ", A286250(n)));
%o A286250 (Scheme)
%o A286250 (define (A286250 n) (A046523 (+ -1 (* 2 (A064216 n)))))
%o A286250 (Python)
%o A286250 from sympy import factorint, prevprime
%o A286250 from operator import mul
%o A286250 def P(n):
%o A286250     f = factorint(n)
%o A286250     return sorted([f[i] for i in f])
%o A286250 def a046523(n):
%o A286250     x=1
%o A286250     while True:
%o A286250         if P(n) == P(x): return x
%o A286250         else: x+=1
%o A286250 def a064216(n):
%o A286250     f=factorint(2*n - 1)
%o A286250     return 1 if n==1 else reduce(mul, [prevprime(i)**f[i] for i in f])
%o A286250 def a(n): return a046523((2*a064216(n)) - 1) # _Indranil Ghosh_, May 13 2017
%Y A286250 Cf. A046523, A064216, A245448, A278223, A286243.
%K A286250 nonn
%O A286250 1,2
%A A286250 _Antti Karttunen_, May 07 2017