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%I #12 Oct 02 2019 20:06:23
%S 0,1,2,6,9,14,33,62,177,414,1155,1719,2625,4018,6849,9770,17675,30206,
%T 90609,164088,336006,757995,1290874,2029875,4059746,7037655,17594075,
%U 50850483,68589598,186888243,373659254
%N Positions of records in A327966.
%C Starting offset is zero to align with the indexing used in A189760, as this is conjecturally also the least k such that A327966(k) = n.
%C For at least n = 1, 3, 4, 5, 6, 7, 10, 14, 15, 17, 18, 21, 23, 24, 25, 26, 27, 28, 29, a(n) = A327965(a(1+n)). For example, 30206 = A327965(90609) and 90609 = A327965(164088).
%C Applying A327968 to these terms yields: 0, 0, 1, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, ...
%C See also comments in A189760.
%o (PARI)
%o A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
%o A327938(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]%f[k,1])); factorback(f); };
%o A327965(n) = if(n<=1,0,A327938(A003415(n)));
%o A327966(n) = if(!n,0,1+A327966(A327965(n)));
%o k=0; n=0; m=-1; while(k<32, if(!(n%2^27),print1("(",n,"),")); if((t=A327966(n))>m, write("b327967.txt", k, " ", n); m = t; k++); n++);
%Y Cf. A327965, A327966.
%Y Differs from A189760 for the first time at n=19, as a(19) = 164088, while A189760(19) = 260343.
%K nonn
%O 0,3
%A _Antti Karttunen_, Oct 01 2019
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