A135058 -id:A135058 - cp's OEIS frontend

A098515 Least m such that m and m+n are both products of exactly n primes counting multiplicity.

1, 2, 4, 27, 36, 675, 810, 12393, 7552, 268992, 506240, 6436341, 2440692, 290698227, 455503986, 4897228800, 520575984, 519417147375, 124730265582, 8961777270765, 753891573760, 203558860750848, 51126160064490, 4021771417157632, 1305269217263592, 69131417822953472, 57710779788427264, 1838459534098563045, 63846774162325476

Offset: 1

Robert G. Wilson v, Sep 11 2004

nonn

			4=2*2 & 6=2*3; 27=3*3*3 & 30=2*3*5; 36=2*2*3*3 & 40=2*2*2*5; 675=3*3*3*5*5 & 680=2*2*2*5*17; 810=2*3*3*3*3*5 and 816=2*2*2*2*3*17; etc.

Cf. A097978.

Cf. A097978, A135058.

f[n_Integer] := Plus @@ Transpose[FactorInteger[n]][[2]]; g[n_] := (k = 2^n; While[a = f[k]; b = f[k + n]; a != b || a != n, k++ ]; k); Do[ Print[ g[n]], {n, 12}]

More terms from David Wasserman, Feb 20 2008

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

Original entry on oeis.org

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

Offset: 0

Lekraj Beedassy, Sep 07 2004

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

			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.

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

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 *)

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

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

More terms from David Wasserman, Feb 19 2008

cp's OEIS Frontend

A098515 Least m such that m and m+n are both products of exactly n primes counting multiplicity.

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