A081084 -id:A081084 - cp's OEIS frontend

A081083 Numbers n such that rad(n+1)=rad(n)+1, where rad(m)=A007947(m) is the squarefree kernel of m.

1, 2, 5, 6, 8, 10, 13, 14, 21, 22, 29, 30, 33, 34, 37, 38, 41, 42, 46, 48, 57, 58, 61, 65, 66, 69, 70, 73, 77, 78, 82, 85, 86, 93, 94, 101, 102, 105, 106, 109, 110, 113, 114, 118, 122, 129, 130, 133, 137, 138, 141, 142, 145, 154, 157, 158, 165, 166, 173, 177, 178, 181

Offset: 1

Reinhard Zumkeller, Mar 04 2003

nonn

Nearly all terms seem to be squarefree, see A081084.

			m=46=2*23=rad(46) and rad(47)=47=46+1=rad(46)+1, therefore 46 is a term;
m=48=3*2^4, rad(48)=6 and rad(49)=rad(7*7)=7=6+1=rad(48)+1, therefore 48 is a term.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007947, A049097.

Union of A007674 and A081084.

rad[n_] := Times @@ (First/@ FactorInteger[n]); s = {}; r1= 1; Do[r2 = rad[n]; If[r2 == r1 +1, AppendTo[s, n-1]]; r1 = r2, {n,2, 182}]; s (* Amiram Eldar, Aug 22 2019 *)

rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])
is(n)=rad(n+1)==rad(n)+1 \\ Charles R Greathouse IV, Aug 08 2013

A075655 Numbers n such that n + product of prime factors of n = (n+1) + product of prime factors of (n+1).

Original entry on oeis.org

3, 24, 1088, 4224, 16640, 66048, 16785408, 67125248, 268468224

Offset: 1

Joseph L. Pe, Oct 12 2002

nonn

Numbers n such that A073353(n) = A073353(n+1). - Michel Marcus, Aug 23 2019

No more terms below 10^10. - Amiram Eldar, Aug 23 2019

			24 + product of prime factors of 24 = 24 + 2 * 3 = 30; 25 + product of prime factors of 25 = 25 + 5 = 30; hence 24 belongs to the sequence.

Cf. A007947, A073353, A081083, A081084.

s[n_] := n + Apply[Times, Transpose[FactorInteger[n]][[1]]]; Select[Range[2, 10^5], s[ # ] == s[ # + 1] &]
Flatten[Position[Partition[Table[n+Times@@Transpose[FactorInteger[ n]] [[1]],{n,2,100000}],2,1],?(#[[1]]==#[[2]]&),{1},Heads->False]]+1 (* _Harvey P. Dale, Apr 20 2014 *)
rad[n_] := Times @@ First /@ FactorInteger[n]; r1 = 1; s = {}; Do[r2 = rad[n]; If[r1 - r2 == 1, AppendTo[s, n-1]]; r1 = r2, {n, 2, 10^5}]; s (* Amiram Eldar, Aug 23 2019 *)

a(7)-a(9) from Amiram Eldar, Aug 23 2019

cp's OEIS Frontend

A081083 Numbers n such that rad(n+1)=rad(n)+1, where rad(m)=A007947(m) is the squarefree kernel of m.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI