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A295888 Filter combining prime signature of n (A101296) with Dedekind's psi (A001615).

%I A295888 #13 Feb 16 2025 08:33:52
%S A295888 1,2,3,4,5,6,7,8,9,10,11,12,13,14,14,15,16,17,18,17,19,20,21,22,23,24,
%T A295888 25,26,27,28,29,30,31,32,31,33,34,35,36,37,38,39,40,41,41,42,43,44,45,
%U A295888 46,42,47,48,49,42,50,51,52,53,54,55,56,57,58,59,60,61,62,56,60,63,64,65,66,67,67,56,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,77
%N A295888 Filter combining prime signature of n (A101296) with Dedekind's psi (A001615).
%H A295888 Antti Karttunen, <a href="/A295888/b295888.txt">Table of n, a(n) for n = 1..65537</a>
%H A295888 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%H A295888 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pairing_function">Pairing Function</a>
%F A295888 Restricted growth sequence transform of function f(n) = (1/2)*(2 + ((A046523(n) + A001615(n))^2) - A046523(n) - 3*A001615(n)), where values A046523(n) and A001615(n) are packed together to a(n) with the 2-argument form of A000027, also known as Cantor pairing-function.
%o A295888 (PARI)
%o A295888 allocatemem(2^30);
%o A295888 up_to = 65537;
%o A295888 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 A295888 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A295888 A001615(n) = (n * sumdivmult(n, d, issquarefree(d)/d)); \\ This function from _Charles R Greathouse IV_, Sep 09 2014
%o A295888 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 A295888 Anotsubmitted8(n) = (1/2)*(2 + ((A046523(n)+A001615(n))^2) - A046523(n) - 3*A001615(n));
%o A295888 write_to_bfile(1,rgs_transform(vector(up_to,n,Anotsubmitted8(n))),"b295888.txt");
%Y A295888 Cf. A001615, A046523, A101296, A291750, A295300, A295880, A295887, A296090.
%K A295888 nonn
%O A295888 1,2
%A A295888 _Antti Karttunen_, Dec 03 2017