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

%I A081083 #14 Aug 22 2019 04:21:22
%S A081083 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 A081083 66,69,70,73,77,78,82,85,86,93,94,101,102,105,106,109,110,113,114,118,
%U A081083 122,129,130,133,137,138,141,142,145,154,157,158,165,166,173,177,178,181
%N A081083 Numbers n such that rad(n+1)=rad(n)+1, where rad(m)=A007947(m) is the squarefree kernel of m.
%C A081083 Nearly all terms seem to be squarefree, see A081084.
%H A081083 Amiram Eldar, <a href="/A081083/b081083.txt">Table of n, a(n) for n = 1..10000</a>
%e A081083 m=46=2*23=rad(46) and rad(47)=47=46+1=rad(46)+1, therefore 46 is a term;
%e A081083 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 A081083 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 A081083 (PARI) rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])
%o A081083 is(n)=rad(n+1)==rad(n)+1 \\ _Charles R Greathouse IV_, Aug 08 2013
%Y A081083 Cf. A007947, A049097.
%Y A081083 Union of A007674 and A081084.
%K A081083 nonn
%O A081083 1,2
%A A081083 _Reinhard Zumkeller_, Mar 04 2003