OFFSET
1,12
COMMENTS
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.
a(n) depends only on prime signature of n (cf. A025487). - Antti Karttunen, Oct 08 2018
LINKS
FORMULA
a(prime^n) = A002846(n).
EXAMPLE
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)
PROG
(PARI)
A064988(n) = { my(f = factor(n)); for (k=1, #f~, f[k, 1] = prime(f[k, 1]); ); factorback(f); }; \\ From A064988
memoA320105 = Map();
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 22 2018
EXTENSIONS
Data section extended to 105 terms by Antti Karttunen, Oct 08 2018
STATUS
approved