A319679 - OEIS

%I #8 Nov 21 2018 09:23:41

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

%H Antti Karttunen, <a href="/A319679/b319679.txt">Table of n, a(n) for n = 1..32769</a>

%o (PARI)

%o up_to = 32769;

%o v268674 = readvec("./b268674_terms_only-32769.txt"); \\ Prepared from the b-file of A268674.

%o A268674(n) = v268674[n];

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

%o 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)));

%Y Cf. A046523, A083221, A268674.

%Y Cf. also A319689.

%K nonn

%O 1,21

%A _Antti Karttunen_, Nov 20 2018