A079617 Occurrences of prime factorization templates, unordered.

1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 5, 1, 3, 3, 6, 1, 5, 1, 5, 3, 3, 1, 7, 2, 3, 4, 5, 1, 8, 1, 9, 3, 3, 3, 10, 1, 3, 3, 7, 1, 8, 1, 5, 5, 3, 1, 11, 2, 5, 3, 5, 1, 7, 3, 7, 3, 3, 1, 12, 1, 3, 5, 13, 3, 8, 1, 5, 3, 8, 1, 14, 1, 3, 5, 5, 3, 8, 1, 11, 6, 3, 1, 12, 3, 3, 3, 7, 1, 12, 3, 5, 3, 3, 3, 15, 1, 5, 5, 10, 1, 8

Offset: 2

Author

Jon Perry, Jan 29 2003

Keywords

• nonn

Comments

1=p, 2=p^2, 3=p.q, 4=p^3, 5=p^2.q, 6=p^4 7=p^3.q, 8=p.q.r, 9=p^5, 10=p^2.q^2, 11=p^4.q

Examples

			Primes are given 1. The next prime factorization pattern is 4=p^2, so a(4)=2 and similarly a(6)=3. a(12)=a(18), etc...
		

Crossrefs

Cf. A037916, A079616.

Programs

PARI

primetemplate2(n)=local(f,fl,fs,res,eres); f=factor(n); fl=length(f[,1]); fs=f[,2]; fs=vecsort(fs); res=""; for (i=1,fl,res=concat(res,fs[i])); eres=eval(res); if (v[eres]==0,v[eres]=vc; vc++); eres vc=1; v=vector(10000); for (j=2,50,print1(v[primetemplate2(j)]","))

Formula

a(n) = A101296(n)-1. - David Wasserman, Dec 27 2004

Extensions

More terms from David Wasserman, Dec 27 2004