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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 31 11:22 EST 2023. Contains 359971 sequences. (Running on oeis4.)