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

2,3

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

Links

Table of n, a(n) for n=2..102.

Formula

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

Example

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...

Prog

(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)]", "))

Crossrefs

Cf. A037916, A079616.

Sequence in context: A249336 A067004 A117920 * A079616 A292587 A336571

Adjacent sequences: A079614 A079615 A079616 * A079618 A079619 A079620

Keyword

nonn

Author

Jon Perry, Jan 29 2003

Extensions

More terms from David Wasserman, Dec 27 2004

Status

approved