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A317145
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Number of maximal chains of factorizations of n into factors > 1, ordered by refinement.
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24
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 1, 7, 1, 1, 1, 5, 1, 3, 1, 2, 2, 1, 1, 15, 1, 2, 1, 2, 1, 5, 1, 5, 1, 1, 1, 11, 1, 1, 2, 11, 1, 3, 1, 2, 1, 3, 1, 26, 1, 1, 2, 2, 1, 3, 1, 15, 2, 1, 1, 11, 1, 1, 1, 5, 1, 11, 1, 2, 1, 1, 1, 52, 1, 2, 2, 7, 1, 3, 1, 5, 3
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OFFSET
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1,12
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COMMENTS
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If x and y are factorizations of the same integer and it is possible to produce x by further factoring the factors of y, flattening, and sorting, then x <= y.
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LINKS
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FORMULA
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EXAMPLE
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The a(36) = 7 maximal chains:
(2*2*3*3) < (2*2*9) < (2*18) < (36)
(2*2*3*3) < (2*2*9) < (4*9) < (36)
(2*2*3*3) < (2*3*6) < (2*18) < (36)
(2*2*3*3) < (2*3*6) < (3*12) < (36)
(2*2*3*3) < (2*3*6) < (6*6) < (36)
(2*2*3*3) < (3*3*4) < (3*12) < (36)
(2*2*3*3) < (3*3*4) < (4*9) < (36)
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PROG
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(PARI)
A064988(n) = { my(f = factor(n)); for (k=1, #f~, f[k, 1] = prime(f[k, 1]); ); factorback(f); }; \\ From A064988
memoA320105 = Map();
A320105(n) = if(bigomega(n)<=2, 1, if(mapisdefined(memoA320105, n), mapget(memoA320105, n), my(f=factor(n), u = #f~, s = 0); for(i=1, u, for(j=i+(1==f[i, 2]), u, s += A320105(prime(primepi(f[i, 1])*primepi(f[j, 1]))*(n/(f[i, 1]*f[j, 1]))))); mapput(memoA320105, n, s); (s)));
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CROSSREFS
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Cf. A001055, A002846, A007716, A045778, A064988, A162247, A213427, A275024, A281113, A299202, A300385, A317144, A317146, A320105.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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