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A097978 a(n) = least m such that m and m+n are both products of exactly n distinct primes. 2
1, 2, 33, 102, 1326, 115005, 31295895, 159282123, 9617162170, 1535531452026, 1960347077019695, 16513791577659519, 271518698440871310 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

LINKS

Table of n, a(n) for n=0..12.

FORMULA

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

EXAMPLE

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.

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 *)

CROSSREFS

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

Sequence in context: A065647 A041127 A282726 * A334197 A156369 A263054

Adjacent sequences:  A097975 A097976 A097977 * A097979 A097980 A097981

KEYWORD

more,nonn

AUTHOR

Lekraj Beedassy, Sep 07 2004

EXTENSIONS

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

More terms from David Wasserman, Feb 19 2008

STATUS

approved

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Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)