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A079616
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Prime factorization templates.
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3
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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
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OFFSET
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1,4
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COMMENTS
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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).
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LINKS
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FORMULA
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EXAMPLE
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Primes are given 1. The next prime factorization pattern is 4=p^2, so a(4)=2 and similarly a(6)=3.
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PROG
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(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)]", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Term a(1) = 0 prepended, superfluous 1 after that removed, extended up to a(105) - Antti Karttunen, Jun 13 2018
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STATUS
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approved
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