A075591 Smallest squarefree number with n prime divisors which is the average of a twin prime pair.

6, 30, 462, 2310, 43890, 1138830, 17160990, 300690390, 15651726090, 239378649510, 12234189897930, 568815710072610, 19835154277048110, 693386350578511590, 37508276737897976010, 3338236629672919864890

Offset

2,1

Links

Table of n, a(n) for n=2..17.

Example

a(4) = 462 because 462 = 2*3*7*11 and the twin primes are 461 and 463.

Mathematica

Generate[pIndex_, i_] := Module[{p2, t}, p2=pIndex; While[p2[[i]]++; Do[p2[[j]]=p2[[i]]+j-i, {j, i+1, Length[p2]}]; t=Times@@Prime[p2]; t<fact*base, AppendTo[s, t]; If[i<Length[p2], Generate[p2, i+1]]]]; fact=3; Table[pin=Range[n]; base=Times@@Prime[pin]; s={base}; Do[Generate[pin, j], {j, n}]; s=Sort[s]; noPrime=True; i=0; While[noPrime&&i<Length[s], i++; noPrime=!(PrimeQ[ -1+s[[i]]] && PrimeQ[1+s[[i]]])]; If[noPrime, -1, s[[i]]], {n, 2, 20}] (T. D. Noe)

Crossrefs

Cf. A075590.

Cf. A073918 (least prime p such that p-1 has exactly n distinct prime factors), A098026 (least prime p such that p+1 has exactly n distinct prime factors).

Sequence in context: A119634 A256545 A349981 * A130075 A066388 A222718

Adjacent sequences: A075588 A075589 A075590 * A075592 A075593 A075594

Keyword

nonn

Author

Amarnath Murthy, Sep 26 2002

Extensions

More terms from T. D. Noe, Dec 13 2004

Status

approved