A108460 -id:A108460 - cp's OEIS frontend

A051707 Number of factorizations of (n,n) into pairs (j,k).

1, 1, 1, 3, 1, 5, 1, 8, 3, 5, 1, 23, 1, 5, 5, 23, 1, 23, 1, 23, 5, 5, 1, 91, 3, 5, 8, 23, 1, 52, 1, 60, 5, 5, 5, 143, 1, 5, 5, 91, 1, 52, 1, 23, 23, 5, 1, 328, 3, 23, 5, 23, 1, 91, 5, 91, 5, 5, 1, 339, 1, 5, 23, 161, 5, 52, 1, 23, 5, 52, 1, 686, 1, 5, 23, 23, 5, 52, 1, 328, 23, 5, 1, 339, 5

Offset: 1

Yasutoshi Kohmoto

Pairs (j,k) must satisfy j>1, k>=1; (a,b)*(x,y)=(a*x,b*y); unit is (1,1).

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)=(2,1)*(3,6)=(2,6)*(3,1)=(2,2)*(3,3)=(2,3)*(3,2), so a(6)=5.

Giovanni Resta, Table of n, a(n) for n = 1..1000

Cf. A050354, A108461, A108455, A348161 (into at most two pairs).
a(A025487) = A108460.
a(p^k) = A108457(k).
a(A002110) = A108459.
Main diagonal of A108455.

Edited by Christian G. Bower, Jun 03 2005

A108467 a(n) = A108466(A025487).

Original entry on oeis.org

1, 1, 2, 3, 4, 11, 9, 35, 25, 20, 55, 106, 132, 45, 222, 303, 566, 100, 808, 918, 827, 339, 1086, 2128, 220, 2682, 4790, 2173, 2453, 4561, 7269, 478, 8335, 21093, 5515, 13223, 17135, 7997, 23079, 1025, 29229, 24503, 22165, 21597, 82298, 13595, 59613, 59196

Offset: 0

Christian G. Bower, Jun 03 2005

nonn

Number of factorizations of (n,n) into pairs (i,j) by prime signature.

Cf. A108460.

More terms from David Wasserman, May 19 2008

cp's OEIS Frontend

A051707 Number of factorizations of (n,n) into pairs (j,k).

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