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A051707 Number of factorizations of (n,n) into pairs (j,k). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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).

LINKS

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

EXAMPLE

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

CROSSREFS

Cf. A050354, A108461. Main diagonal of A108455. a(A025487)=A108460. a(p^k)=A108457(k). a(A002110)=A108459.

Sequence in context: A050329 A147005 A254577 * A302787 A240535 A262397

Adjacent sequences:  A051704 A051705 A051706 * A051708 A051709 A051710

KEYWORD

nonn,nice,easy

AUTHOR

Yasutoshi Kohmoto

EXTENSIONS

Edited by Christian G. Bower, Jun 03 2005

STATUS

approved

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Last modified April 23 18:12 EDT 2019. Contains 322387 sequences. (Running on oeis4.)