A319337 - OEIS

%I #6 Sep 24 2018 17:46:19

%S 1,2,3,4,3,5,3,6,7,5,3,8,3,5,9,10,3,8,3,11,9,5,3,12,4,5,13,11,3,14,3,

%T 15,9,5,9,16,3,5,9,12,3,14,3,11,17,5,3,18,4,11,9,11,3,19,9,12,9,5,3,

%U 20,3,5,17,21,9,14,3,11,9,14,3,22,3,5,17,11,9,14,3,23,10,5,3,20,9,5,9,12,3,24,9,11,9,5,9,25,3,11,17,26,3,14,3,12,27

%N Filter sequence combining gcd(n,tau(n)) (= A009191) with the prime signature of n (A046523).

%C Restricted growth sequence transform of ordered pair [A009191(n), A046523(n)].

%H Antti Karttunen, <a href="/A319337/b319337.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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 A009191(n) = gcd(n, numdiv(n));

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p=0); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };

%o v319337 = rgs_transform(vector(up_to,n,[A009191(n),A046523(n)]));

%o A319337(n) = v319337[n];

%Y Cf. A009191, A046523, A101296, A300230, A300240, A305801, A319338.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 24 2018