A097978 -id:A097978 - 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

A135058 Least m such that both m and m+n have exactly n distinct prime divisors, ignoring multiplicity.

Original entry on oeis.org

1, 2, 10, 102, 1326, 96135, 607614, 159282123, 9617162170, 1110180535035, 28334309296920, 16513791577659519, 271518698440871310

Offset: 0

David Wasserman, Feb 11 2008

Note that here the m and m+n may be divisible by squares (compare A097978).
a(13) <= 592357638037885411965.
If we change "exactly n" to "at least n", the sequence is still the same at least through a(12).

			a(2) = 10 because 10=2*5 and 12=3*2^2 have two distinct prime factors.
a(3) = 102 because 102=2*3*17 and 105=3*5*7 each have three distinct prime factors.
a(5) = 96135 because 96135 = 3*5*13*17*29 and 96140 = 2^2*5*11*19*23 each have 5 distinct prime factors.

Cf. A097978, A098515.

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

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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