cp's OEIS Frontend

A305899 Filter sequence related to factorization ("prime") signatures of Stern polynomials when factored over Z.

%I A305899 #8 Jul 01 2018 08:35:53
%S A305899 1,2,2,3,2,4,2,5,3,4,2,6,2,4,4,7,2,6,2,6,4,4,2,8,2,4,5,6,2,9,2,10,4,4,
%T A305899 4,11,2,4,4,8,2,9,2,6,6,4,2,12,3,4,4,6,2,8,2,8,4,4,2,13,2,4,9,14,2,9,
%U A305899 2,6,4,9,2,15,2,4,6,6,2,9,2,12,4,4,2,13,4,4,4,8,2,13,2,6,4,4,2,16,2,6,6,6,2,9,2,8,9
%N A305899 Filter sequence related to factorization ("prime") signatures of Stern polynomials when factored over Z.
%C A305899 Restricted growth sequence transform of A284011.
%H A305899 Antti Karttunen, <a href="/A305899/b305899.txt">Table of n, a(n) for n = 1..65537</a>
%o A305899 (PARI)
%o A305899 up_to = 65537;
%o A305899 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A305899 pfps(n) = { my(f=factor(n)); sum(i=1, #f~, f[i, 2] * 'x^(primepi(f[i, 1])-1)); };
%o A305899 A284010(n) = { if(!bitand(n, (n-1)), 0, my(p=0, f=vecsort(factor(pfps(n))[, 2], ,4)); prod(i=1, #f, (p=nextprime(p+1))^f[i])); }
%o A305899 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From _Michel Marcus_
%o A305899 A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));
%o A305899 A284011(n) = A284010(A260443(n));
%o A305899 v305899 = rgs_transform(vector(up_to, n, A284011(n)));
%o A305899 A305899(n) = v305899[n];
%Y A305899 Cf. A260443, A284011, A305898.
%Y A305899 Cf. also A304751.
%K A305899 nonn
%O A305899 1,2
%A A305899 _Antti Karttunen_, Jul 01 2018