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A319353 Filter sequence combining weights of partitions with Heinz-numbers equal to the proper divisors of n.

%I A319353 #8 Sep 17 2018 15:46:02
%S A319353 1,2,2,3,2,4,2,4,5,6,2,7,2,8,9,10,2,11,2,11,12,13,2,14,15,16,12,17,2,
%T A319353 18,2,11,19,20,21,22,2,23,24,18,2,25,2,26,27,28,2,29,30,31,32,33,2,25,
%U A319353 34,25,35,36,2,37,2,38,39,40,41,42,2,43,44,45,2,37,2,46,47,48,49,50,2,51,52,53,2,54,55,56,57,42,2,58,59,60,61,62,63,37,2,64,65
%N A319353 Filter sequence combining weights of partitions with Heinz-numbers equal to the proper divisors of n.
%C A319353 Restricted growth sequence transform of A319352.
%C A319353 For all i, j:
%C A319353   a(i) = a(j) => A301855(i) = A301855(j).
%C A319353   a(i) = a(j) => A304793(i) = A304793(j).
%H A319353 Antti Karttunen, <a href="/A319353/b319353.txt">Table of n, a(n) for n = 1..65537</a>
%o A319353 (PARI)
%o A319353 up_to = 65537;
%o A319353 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 A319353 A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
%o A319353 A319352(n) = { my(m=1); fordiv(n, d, if(d<n, m *= prime(1+A056239(d)))); (m); };
%o A319353 v319353 = rgs_transform(vector(up_to,n,A319352(n)));
%o A319353 A319353(n) = v319353[n];
%Y A319353 Cf. A056239, A319352.
%K A319353 nonn
%O A319353 1,2
%A A319353 _Antti Karttunen_, Sep 17 2018