A050347 -id:A050347 - cp's OEIS frontend

A050348 Number of factorizations into distinct factors with 2 levels of parentheses indexed by prime signatures. A050347(A025487).

1, 1, 1, 4, 4, 10, 7, 26, 22, 14, 34, 63, 74, 29, 105, 143, 223, 57, 296, 312, 320, 154, 366, 617, 110, 769, 1087, 697, 641, 1136, 1589, 217, 1906, 3394, 1483, 2224, 3246, 1562, 3919, 417, 4251, 4561, 3175, 3858, 9736, 3111, 6910, 8772, 6183, 9327, 794

Offset: 1

Christian G. Bower, Oct 15 1999

nonn

A050349 Number of ways to factor n into distinct factors with 3 levels of parentheses.

Original entry on oeis.org

1, 1, 1, 1, 1, 5, 1, 5, 1, 5, 1, 15, 1, 5, 5, 11, 1, 15, 1, 15, 5, 5, 1, 45, 1, 5, 5, 15, 1, 35, 1, 25, 5, 5, 5, 65, 1, 5, 5, 45, 1, 35, 1, 15, 15, 5, 1, 130, 1, 15, 5, 15, 1, 45, 5, 45, 5, 5, 1, 145, 1, 5, 15, 60, 5, 35, 1, 15, 5, 35, 1, 240, 1, 5, 15, 15, 5, 35, 1, 130, 11, 5, 1, 145, 5

Offset: 1

Christian G. Bower, Oct 15 1999

nonn

a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).

			6 = (((6))) = (((3*2))) = (((3)*(2))) = (((3))*((2))) = (((3)))*(((2))).

R. J. Mathar, Table of n, a(n) for n = 1..1727

Cf. A045778, A050345-A050350. a(p^k)=A050344. a(A002110)=A000357.

Dirichlet g.f.: Product_{n>=2}(1+1/n^s)^A050347(n).

a(n) = A050350(A101296(n)). - R. J. Mathar, May 26 2017

cp's OEIS Frontend

A050348 Number of factorizations into distinct factors with 2 levels of parentheses indexed by prime signatures. A050347(A025487).

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A050349 Number of ways to factor n into distinct factors with 3 levels of parentheses.

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