A322607 Numbers that can be expressed as the ratio between the product and the sum of consecutive squarefree numbers starting from 1.

1, 3080, 350350, 61850250, 17823180375, 6871260396000, 88909822914869880000, 2746644314348614680000, 2980109081068246927800000, 9638057975990853416623724908800000, 424217819372970387341691005411520000, 51912228216508515627667235880347808000000, 152157812632066726080765311397008321568000000

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Formula

a(n) = A111059(A322608(n+1))/A173143(A322608(n+1)).

Example

1 is a term because 1/1 = (1*2*3)/(1+2+3) = 1.
3080 is a term because (1*2*3*5*6*7*10*11)/(1+2+3+5+6+7+10+11) = 138600/45 = 3080.

Maple

with(numtheory): P:=proc(q) local a, b, c, n; a:=1; b:=0; c:=[];
for n from 1 to q do if issqrfree(n) then a:=a*n; b:=b+n;
if frac(a/b)=0 then if n>1 then c:=[op(c), a/b];
fi; fi; fi; od; op(c); end: P(60);

Crossrefs

Cf. A005117, A111059, A116536, A141092, A173143, A322608.

Sequence in context: A205358 A045083 A186470 * A284660 A234781 A045079

Adjacent sequences: A322604 A322605 A322606 * A322608 A322609 A322610

Keyword

nonn,easy

Author

Paolo P. Lava, Dec 20 2018

Status

approved