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A305898 Filter sequence combining prime signature of n (A046523) and similar signature (A284011) obtained when Stern polynomial B(n,x) is factored over Z.

%I A305898 #6 Jul 01 2018 08:35:46
%S A305898 1,2,2,3,2,4,2,5,3,4,2,6,2,4,4,7,2,6,2,6,4,4,2,8,9,4,5,6,2,10,2,11,4,
%T A305898 4,4,12,2,4,4,8,2,10,2,6,6,4,2,13,3,14,4,6,2,8,15,8,4,4,2,16,2,4,17,
%U A305898 18,15,10,2,6,4,10,2,19,2,4,6,6,15,10,2,13,20,4,2,16,4,4,4,8,2,16,15,6,4,4,15,21,2,6,6,22,2,10,2,8,10
%N A305898 Filter sequence combining prime signature of n (A046523) and similar signature (A284011) obtained when Stern polynomial B(n,x) is factored over Z.
%C A305898 Restricted growth sequence transform of ordered pair [A046523(n), A284011(n)].
%C A305898 For all i, j: a(i) = a(j) => A305892(i) = A305892(j).
%H A305898 Antti Karttunen, <a href="/A305898/b305898.txt">Table of n, a(n) for n = 1..65537</a>
%o A305898 (PARI)
%o A305898 up_to = 65537;
%o A305898 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 A305898 pfps(n) = { my(f=factor(n)); sum(i=1, #f~, f[i, 2] * 'x^(primepi(f[i, 1])-1)); };
%o A305898 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 A305898 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A305898 A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));
%o A305898 A284011(n) = A284010(A260443(n));
%o A305898 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305898 Aux305898(n) = [A046523(n), A284011(n)];
%o A305898 v305898 = rgs_transform(vector(up_to, n, Aux305898(n)));
%o A305898 A305898(n) = v305898[n];
%Y A305898 Cf. A046523, A284011, A305892, A305899.
%Y A305898 Cf. also A305790.
%K A305898 nonn
%O A305898 1,2
%A A305898 _Antti Karttunen_, Jul 01 2018