A319694 Product of A078899(x) for all x encountered when map x -> A252463(x) is iterated, starting from x = A252463(n); a(1) = 1.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 6, 1, 6, 1, 2, 2, 1, 1, 8, 6, 1, 6, 2, 1, 6, 1, 24, 2, 1, 6, 30, 1, 1, 2, 8, 1, 6, 1, 2, 8, 1, 1, 48, 30, 30, 2, 2, 1, 42, 6, 8, 2, 1, 1, 36, 1, 1, 8, 120, 6, 6, 1, 2, 2, 30, 1, 240, 1, 1, 30, 2, 30, 6, 1, 56, 24, 1, 1, 36, 6, 1, 2, 8, 1, 64, 30, 2, 2, 1, 6, 432, 1, 210, 8, 270, 1, 6, 1, 8, 36

Offset: 1

Author

Antti Karttunen, Nov 21 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A005940, A078899, A252463.

Cf. also A319689.

Programs

PARI

up_to = 16384;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
v078899 = ordinal_transform(vector(up_to,n,A006530(n)));
A078899(n) = v078899[n];
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A252463(n) = if(!(n%2),n/2,A064989(n));
A319694(n) = { my(m=1); while(1<(n=A252463(n)), m *= A078899(n)); (m); };