A079616 Prime factorization templates.

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, 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, 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

Offset: 1

Author

Jon Perry, Jan 29 2003

Keywords

• nonn

Comments

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

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A037916, A077462.

Programs

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)]","))

PARI

A079616(n) = (A077462(n)-1); \\ Antti Karttunen, Jun 13 2018, uses code in A077462.

Formula

a(n) = A077462(n) - 1. - David Wasserman, Dec 21 2004

Extensions

More terms from David Wasserman, Dec 21 2004

Term a(1) = 0 prepended, superfluous 1 after that removed, extended up to a(105) - Antti Karttunen, Jun 13 2018

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