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%I #5 Jul 01 2018 08:35:38
%S 1,2,3,4,3,5,3,6,7,8,3,9,3,10,10,11,3,12,3,13,10,8,3,14,7,10,15,16,3,
%T 17,3,18,10,10,10,19,3,10,10,20,3,21,3,22,23,8,3,24,7,23,10,16,3,25,
%U 10,26,10,8,3,27,3,10,23,28,10,17,3,23,10,17,3,29,3,10,23,23,10,17,3,30,31,8,3,32,10,10,10,33,3,34,10,22,10,10,10,35,3,23,23,36
%N Filter sequence combining prime signature of n (A046523) and the cardinality of invphi (A014197).
%C Restricted growth sequence transform of ordered pair [A046523(n), A014197(n)].
%C For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A097946(i) = A097946(j).
%H Antti Karttunen, <a href="/A305896/b305896.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 A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))} \\ This function from _M. F. Hasler_, Oct 05 2009
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o Aux305896(n) = [A046523(n), A014197(n)];
%o v305896 = rgs_transform(vector(up_to, n, Aux305896(n)));
%o A305896(n) = v305896[n];
%Y Cf. A014197, A046523, A305801.
%Y Cf. also A097946.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 01 2018
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