A319679 Number of distinct prime signatures that occur when map x -> A268674(x) is iterated, starting from x = n, until an even number is reached; a(1) = 0 by convention.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2

Offset: 1

Author

Antti Karttunen, Nov 20 2018

Keywords

• nonn

Comments

Number of distinct values that A046523 obtains when applied to n and all the terms above it in that column where it is located in array A083221.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32769

Crossrefs

Cf. A046523, A083221, A268674.

Cf. also A319689.

Programs

PARI

up_to = 32769;
v268674 = readvec("./b268674_terms_only-32769.txt"); \\ Prepared from the b-file of A268674.
A268674(n) = v268674[n];
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A319679(n) = if(1==n,0,my(m=Map(),s,k=0); while(1,if(!mapisdefined(m,s=A046523(n)), mapput(m,s,s); k++); if(!(n%2), return(k)); n = A268674(n)));