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

0,3

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.

Links

Table of n, a(n) for n=0..30.

Prog

(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++);

Crossrefs

Cf. A327965, A327966.

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

Sequence in context: A217001 A320666 A079023 * A189760 A363373 A353083

Adjacent sequences: A327964 A327965 A327966 * A327968 A327969 A327970

Keyword

nonn

Author

Antti Karttunen, Oct 01 2019

Status

approved