A140862 Incorrect duplicate of A081083.
1, 2, 5, 6, 2, 8, 10, 13, 14, 22, 30, 33, 37, 41, 42, 46, 48, 57, 58, 61, 65, 66, 69, 70, 73, 78
Offset: 1
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
48 = 2^4*3 is in the sequence because it is not squarefree, its squarefree kernel is 6 and the squarefree kernel of 49 = 7^2 is 7.
with(numtheory): rad:=proc(n) local fs, c: fs:=convert(factorset(n),list): c:=nops(fs): product(fs[j],j=1..c) end: b:=proc(n) if mobius(n)=0 and rad(n+1)=rad(n)+1 then n else fi end:seq(b(n),n=1..1000); # Emeric Deutsch
rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i]) is(n)=!issquarefree(n) && rad(n+1)==rad(n)+1 \\ Charles R Greathouse IV, Aug 08 2013
rad(n) = factorback(factorint(n)[, 1]); \\ A007947 lista(nn) = {for (n=1, nn, my(p=rad(n)); if (isprime(p) && isprime(p+6) && (p+1==rad(n+1)), print1(p, ", ")););} \\ Michel Marcus, Aug 22 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.
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 *)
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