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

Author

Paolo P. Lava, Dec 20 2018

Keywords

• nonn
• easy

Examples

			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.
		

Crossrefs

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

Programs

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);

Formula

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