A079892 -id:A079892 - cp's OEIS frontend

A079893 a(n) = gcd(n, A079892(n)), where A079892(n) is the least number > n having one more distinct prime factor than n.

1, 2, 3, 2, 1, 6, 1, 2, 1, 10, 1, 6, 1, 2, 15, 2, 1, 6, 1, 10, 3, 2, 1, 6, 1, 2, 1, 2, 1, 30, 1, 1, 3, 2, 7, 6, 1, 2, 3, 2, 1, 42, 1, 4, 15, 2, 1, 12, 1, 10, 3, 4, 1, 6, 5, 4, 3, 2, 1, 30, 1, 2, 3, 1, 1, 6, 1, 2, 1, 70, 1, 6, 1, 2, 3, 2, 1, 6, 1, 4, 1, 2, 1, 42, 5, 2, 3, 2, 1, 30, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2

Offset: 1

Reinhard Zumkeller, Jan 14 2003

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A079891, A079894.

A079893(n) = { my(x=1+omega(n)); for(k=1+n, oo, if(omega(k)==x, return(gcd(k,n)))); }; \\ Antti Karttunen, Mar 02 2023

A079894 a(n) = gcd(A079890(n), A079892(n)).

Original entry on oeis.org

2, 2, 2, 2, 6, 2, 1, 2, 2, 6, 2, 2, 14, 6, 6, 2, 3, 6, 1, 6, 3, 3, 1, 2, 1, 3, 4, 6, 33, 6, 33, 1, 42, 42, 42, 6, 38, 42, 42, 6, 2, 6, 2, 6, 6, 10, 1, 4, 50, 6, 4, 6, 1, 12, 3, 12, 3, 3, 62, 6, 62, 3, 3, 1, 66, 3, 1, 1, 70, 3, 2, 6, 74, 3, 3, 3, 78, 3, 2, 12, 2, 4, 85, 6, 2, 2, 2, 18, 91, 6, 2, 2, 2, 2

Offset: 1

Reinhard Zumkeller, Jan 14 2003

nonn

Cf. A079891, A079893.

A079890 Least number > n having one more prime factor than n, not necessarily distinct.

Original entry on oeis.org

2, 4, 4, 8, 6, 8, 9, 16, 12, 12, 14, 16, 14, 18, 18, 32, 21, 24, 21, 24, 27, 27, 25, 32, 27, 27, 36, 36, 33, 36, 33, 64, 42, 42, 42, 48, 38, 42, 42, 48, 46, 54, 46, 54, 54, 50, 49, 64, 50, 54, 52, 54, 55, 72, 63, 72, 63, 63, 62, 72, 62, 63, 81, 128, 66, 81, 69, 81, 70, 81, 74, 96

Offset: 1

Reinhard Zumkeller, Jan 14 2003

A001222(a(n)) = A001222(n) + 1;
a(2^k) = 2^(k+1).
a(A076156(n)) = A076156(n)+1. - Reinhard Zumkeller, Feb 01 2008

R. Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A079891, A079892.

Cf. A165712.

a079890 n = head [x | x <- [n + 1 ..], a001222 x == 1 + a001222 n]
-- Reinhard Zumkeller, Aug 29 2013

lng[n_]:=Module[{x=n+1,pon=PrimeOmega[n]},While[PrimeOmega[x]-pon!=1, x++]; x]; Array[lng,80] (* Harvey P. Dale, Nov 09 2011 *)

A165713 a(n) = the smallest integer > n that is divisible by exactly the same number of distinct primes as n is.

Original entry on oeis.org

3, 4, 5, 7, 10, 8, 9, 11, 12, 13, 14, 16, 15, 18, 17, 19, 20, 23, 21, 22, 24, 25, 26, 27, 28, 29, 33, 31, 42, 32, 37, 34, 35, 36, 38, 41, 39, 40, 44, 43, 60, 47, 45, 46, 48, 49, 50, 53, 51, 52, 54, 59, 55, 56, 57, 58, 62, 61, 66, 64, 63, 65, 67, 68, 70, 71, 69, 72, 78, 73, 74

Offset: 2

Leroy Quet, Sep 24 2009

nonn

			12 = 2^2 *3, and so is divisible by exactly 2 distinct primes. The next larger number divisible by exactly 2 distinct primes is 14, which is 2*7. So a(12) = 14.

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Cf. A165712, A137929.

Cf. A001221, A079892.

a165713 n = head [x | x <- [n + 1 ..], a001221 x == a001221 n]
-- Reinhard Zumkeller, Aug 29 2013

a[n_] := For[nu = PrimeNu[n]; k = n+1, True, k++, If[PrimeNu[k] == nu, Return[k]]]; Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Nov 18 2013 *)

More terms from Sean A. Irvine, Feb 10 2010

cp's OEIS Frontend

A079893 a(n) = gcd(n, A079892(n)), where A079892(n) is the least number > n having one more distinct prime factor than n.

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A079894 a(n) = gcd(A079890(n), A079892(n)).

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A079890 Least number > n having one more prime factor than n, not necessarily distinct.

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A165713 a(n) = the smallest integer > n that is divisible by exactly the same number of distinct primes as n is.

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