A327967 Positions of records in A327966.

0, 1, 2, 6, 9, 14, 33, 62, 177, 414, 1155, 1719, 2625, 4018, 6849, 9770, 17675, 30206, 90609, 164088, 336006, 757995, 1290874, 2029875, 4059746, 7037655, 17594075, 50850483, 68589598, 186888243, 373659254

Offset: 0

Author

Antti Karttunen, Oct 01 2019

Keywords

• nonn

Comments

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.

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).

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, ...

See also comments in A189760.

Crossrefs

Cf. A327965, A327966.

Differs from A189760 for the first time at n=19, as a(19) = 164088, while A189760(19) = 260343.

Programs

PARI

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
A327938(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]%f[k,1])); factorback(f); };
A327965(n) = if(n<=1,0,A327938(A003415(n)));
A327966(n) = if(!n,0,1+A327966(A327965(n)));
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++);