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Numbers n such that rad(n+1)=rad(n)+1, where rad(m)=A007947(m) is the squarefree kernel of m.
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%I #14 Aug 22 2019 04:21:22

%S 1,2,5,6,8,10,13,14,21,22,29,30,33,34,37,38,41,42,46,48,57,58,61,65,

%T 66,69,70,73,77,78,82,85,86,93,94,101,102,105,106,109,110,113,114,118,

%U 122,129,130,133,137,138,141,142,145,154,157,158,165,166,173,177,178,181

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

%C Nearly all terms seem to be squarefree, see A081084.

%H Amiram Eldar, <a href="/A081083/b081083.txt">Table of n, a(n) for n = 1..10000</a>

%e m=46=2*23=rad(46) and rad(47)=47=46+1=rad(46)+1, therefore 46 is a term;

%e 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.

%t 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 *)

%o (PARI) rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])

%o is(n)=rad(n+1)==rad(n)+1 \\ _Charles R Greathouse IV_, Aug 08 2013

%Y Cf. A007947, A049097.

%Y Union of A007674 and A081084.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 04 2003