%I #15 Jun 13 2018 23:10:30

%S 0,1,1,2,1,3,1,4,2,3,1,5,1,3,3,6,1,7,1,5,3,3,1,8,2,3,4,5,1,9,1,10,3,3,

%T 3,11,1,3,3,8,1,9,1,5,5,3,1,12,2,7,3,5,1,13,3,8,3,3,1,14,1,3,5,15,3,9,

%U 1,5,3,9,1,16,1,3,7,5,3,9,1,12,6,3,1,14,3,3,3,8,1,17,3,5,3,3,3,18,1,7,5,11,1,9,1,8,9

%N Prime factorization templates.

%C 0 = 1, 1 = p, 2 = p^2, 3 = p.q, 4 = p^3, 5 = p^2.q, 6 = p^4, 7 = p.q^2, 8 = p^3.q, 9 = p.q.r, 10 = p^5, 11 = p^2.q^2, 12 = p^4.q (p<q<r).

%H Antti Karttunen, <a href="/A079616/b079616.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = A077462(n) - 1. - _David Wasserman_, Dec 21 2004

%e Primes are given 1. The next prime factorization pattern is 4=p^2, so a(4)=2 and similarly a(6)=3.

%o (PARI) primetemplate(n)=local(f,fl,res,eres); f=factor(n); fl=length(f[,1]); res=""; for (i=1,fl,res=concat(res,f[,2][i])); eres=eval(res); if (v[eres]==0,v[eres]=vc; vc++); eres vc=1; v=vector(10000); for (j=2,50,print1(v[primetemplate(j)]","))

%o (PARI) A079616(n) = (A077462(n)-1); \\ _Antti Karttunen_, Jun 13 2018, uses code in A077462.

%Y Cf. A037916, A077462.

%K nonn

%O 1,4

%A _Jon Perry_, Jan 29 2003

%E More terms from _David Wasserman_, Dec 21 2004

%E Term a(1) = 0 prepended, superfluous 1 after that removed, extended up to a(105) - _Antti Karttunen_, Jun 13 2018