A376421 - OEIS

%I #7 Sep 23 2024 13:37:32

%S 24,42,48,50,54,60,75,78,100,102,108,110,112,114,120,126,150,156,162,

%T 165,168,170,174,180,186,189,190,192,198,200,204,210,216,220,222,224,

%U 225,228,230,231,234,238,240,242,245,250,294,300,312,315,318,324,330,336

%N Numbers m with largest nondivisor k <= m such that rad(k) | m is not a prime power, where rad = A007947.

%C The term prime power used here refers to k in A246547.

%C Includes m such that the largest k = A373736(m) in row m of A272618 is not in A246547.

%C Subset of A024619, since for prime powers m = p^e, e >= 1, all k <= m such that rad(k) | m also divide m.

%C Contains A376422, since nondivisor k such that rad(k) | m must be composite, and composite prime powers m in A246547 are a subset of A001694.

%H Michael De Vlieger, <a href="/A376421/b376421.txt">Table of n, a(n) for n = 1..32299</a>

%e 6 is not included since nondivisor 4 = 2^2 is such that rad(4) | 6, but 4 is a perfect power of a prime.

%e 24 is included since nondivisor 18 = 2 * 3^2 is such that rad(18) | 24 and is not a prime power.

%e 42 is included since nondivisor 36 = 2^2 * 3^2 is such that rad(36) | 42 and 36 is not a prime power.

%e 60 is in the sequence because nondivisor 54 = 2 * 3^3 but rad(54) | 60 and 54 is not a prime power, etc.

%t rad[x_] := Times @@ FactorInteger[x][[All, 1]];

%t Table[If[PrimePowerQ[n], Nothing,

%t   If[PrimePowerQ[#], Nothing, n] &@

%t    SelectFirst[Range[n - 1, 1, -1],

%t     And[! Divisible[n, #], Divisible[n, rad[#]]] &] ], {n, 2, 336}]

%Y Cf. A024619, A007947, A246547, A272618, A373736, A376422.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Sep 22 2024