A097978 a(n) = least m such that m and m+n are both products of exactly n distinct primes.

1, 2, 33, 102, 1326, 115005, 31295895, 159282123, 9617162170, 1535531452026, 1960347077019695, 16513791577659519, 271518698440871310

Offset: 0

Author

Lekraj Beedassy, Sep 07 2004

Keywords

• more
• nonn

Comments

Note that a(n) and a(n)+n are required to be squarefree (compare A135058). - David Wasserman, Feb 19 2008

If we change "exactly n" to "at least n", the sequence is still the same at least through a(12). - David Wasserman, Feb 19 2008

a(13) <= 592357638037885411965. - David Wasserman, Feb 19 2008

Examples

			a(2) = 33  because 33 and 35 are both in A006881.
a(3) = 102 because 102 and 105 are both in A007304.
a(4) = 1326 because 1326 and 1330 are both in A046386.
		

Crossrefs

Cf. A098515. A135058 (without regard to multiplicity).

Programs

Mathematica

f[n_] := Block[{lst = FactorInteger[n], a, b}, a = Plus @@ Last /@ lst; b = Length[lst]; If[a == b, b, 0]]; g[n_] := Block[{k = Product[ Prime[i], {i, n}]}, While[ f[k] != n || f[k] != f[k + n], k++ ]; k]; Do[ Print[ g[n]], {n, 1, 6}] (* Robert G. Wilson v, Sep 11 2004 *)

Formula

a(n) = min{m: A001221(m) = A001222(m) = A001221(m+n) = A001222(m+n)= n}. - R. J. Mathar, Mar 01 2017

Extensions

Edited and extended by Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004

More terms from David Wasserman, Feb 19 2008