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

1,2

Comments

Nearly all terms seem to be squarefree, see A081084.

Links

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

Example

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.

Mathematica

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 *)

Prog

(PARI) 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

Crossrefs

Cf. A007947, A049097.

Union of A007674 and A081084.

Sequence in context: A047441 A284777 A344312 * A288635 A308595 A104493

Adjacent sequences: A081080 A081081 A081082 * A081084 A081085 A081086

Keyword

nonn

Author

Reinhard Zumkeller, Mar 04 2003

Status

approved