A073840 -id:A073840 - cp's OEIS frontend

A157625 Product of the composite numbers between n+1 and 2n, both inclusive.

1, 4, 24, 48, 4320, 8640, 120960, 3628800, 7257600, 14515200, 6706022400, 13412044800, 8717829120000, 470762772480000, 941525544960000, 1883051089920000, 2112783322890240000, 147894832602316800000

Offset: 1

Jaume Oliver Lafont, Mar 03 2009

nonn

This function is very useful in a problem due to Paul Erdős recorded in A157017. - M. F. Hasler, Feb 26 2014

Cf. A073840, A157017, A144186 (product of primes between n+2 and 2n, both inclusive).

nn=20;With[{comps=Complement[Range[2nn],Prime[Range[PrimePi[2nn]]]]}, Table[ Times@@ Select[comps,#>n&&#<=2n&],{n,nn}]] (* Harvey P. Dale, Feb 18 2013 *)

PARI
```
a(n)=prod(i=n+1,2*n,if(isprime(i),1,i))
```

a(n) = n!*A000984(n)*A034386(n)/A034386(2n). - M. F. Hasler, Feb 26 2014

A073839 Sum of the composite numbers between n and 2n (both inclusive).

Original entry on oeis.org

0, 4, 10, 18, 33, 45, 53, 84, 94, 105, 138, 162, 201, 256, 272, 289, 340, 411, 431, 510, 532, 555, 624, 672, 747, 825, 853, 937, 1024, 1084, 1116, 1243, 1342, 1377, 1482, 1519, 1557, 1708, 1825, 1866, 1989, 2073, 2202, 2377, 2423, 2561, 2702, 2893, 2943

Offset: 1

Amarnath Murthy, Aug 13 2002

nonn

a(n) is the sum of A075084(n) composite numbers (A002808). - Michel Marcus, Aug 26 2015

			a(6) = 6+8+9+10+12 = 45.

Cf. A002808, A073840, A075084.

for n from 1 to 150 do l := 0:for j from n to 2*n do if not isprime(j) then l := l+j:fi:od:a[n] := l:od:a[1] := 0:seq(a[j],j=1..150);

cs[x_] := Flatten[Position[Table[PrimeQ[j], {j, x, 2*x}], False]]+x-1; sucs[x_] := Apply[Plus, cs[x]]; Table[sucs[w], {w, 1, 128}]
Join[{0}, Table[Plus @@ Select[Range[n, 2 n], ! PrimeQ[#] &], {n, 2, 49}]] (* Jayanta Basu, Aug 12 2013 *)

a(n) = my(s=0); forcomposite (c=n, 2*n, s+=c); s; \\ Michel Marcus, Aug 26 2015

More terms from Sascha Kurz and Labos Elemer, Aug 14 2002

cp's OEIS Frontend

A157625 Product of the composite numbers between n+1 and 2n, both inclusive.

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