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A079617
Occurrences of prime factorization templates, unordered.
0
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
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
Sequence in context: A249336 A067004 A117920 * A079616 A292587 A336571
KEYWORD
nonn
AUTHOR
Jon Perry, Jan 29 2003
EXTENSIONS
More terms from David Wasserman, Dec 27 2004
STATUS
approved