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A079616
Prime factorization templates.
3
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
1,4
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<q<r).
LINKS
FORMULA
a(n) = A077462(n) - 1. - David Wasserman, Dec 21 2004
EXAMPLE
Primes are given 1. The next prime factorization pattern is 4=p^2, so a(4)=2 and similarly a(6)=3.
PROG
(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.
CROSSREFS
Sequence in context: A067004 A117920 A079617 * A292587 A336571 A334032
KEYWORD
nonn
AUTHOR
Jon Perry, Jan 29 2003
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
STATUS
approved