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A296090 Filter combining the sum of divisors (A000203) and prime-signature (A101296) of n; restricted growth sequence transform of A286360.

%I A296090 #9 Dec 07 2017 22:21:19
%S A296090 1,2,3,4,5,6,7,8,9,10,11,12,13,14,14,15,16,17,18,19,20,21,22,23,24,25,
%T A296090 26,27,28,29,30,31,32,33,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
%U A296090 48,44,49,50,51,44,51,52,53,54,55,56,57,58,59,60,61,62,63,57,61,64,65,66,67,68,69,57,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,79
%N A296090 Filter combining the sum of divisors (A000203) and prime-signature (A101296) of n; restricted growth sequence transform of A286360.
%C A296090 For all i, j:
%C A296090   a(i) = a(j) => A286034(i) = A286034(j).
%C A296090   a(i) = a(j) => A295880(i) = A295880(j).
%H A296090 Antti Karttunen, <a href="/A296090/b296090.txt">Table of n, a(n) for n = 1..65537</a>
%o A296090 (PARI)
%o A296090 up_to = 65537;
%o A296090 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 A296090 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A296090 A000203(n) = sigma(n);
%o A296090 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 A296090 A286360(n) = (1/2)*(2 + ((A046523(n)+A000203(n))^2) - A046523(n) - 3*A000203(n));
%o A296090 write_to_bfile(1,rgs_transform(vector(up_to,n,A286360(n))),"b296090.txt");
%Y A296090 Cf. A000203, A101296, A046523, A286034, A286360, A295300, A295888, A296089.
%Y A296090 Differs from related A295880 for the first time at n=135, where a(135) = 123, while A295880(135) = 104.
%K A296090 nonn
%O A296090 1,2
%A A296090 _Antti Karttunen_, Dec 07 2017