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%I #30 Apr 23 2023 22:43:52
%S 42,66,78,362,1086,1122,1254,1794,1810,1846,1974,2534,2730,3318,3982,
%T 4890,5538,5590,6006,6214,9230,12922,12990,13515,15510,16205,17430,
%U 18642,20306,22170,23170,25098,26962,27030,29274,31070,32142,32410
%N Squarefree composite numbers m such that k - m^2 < m, where k is the smallest number greater than m^2 such that rad(k) | m.
%C Most small squarefree m have k - m^2 > m. For prime m = p, k = p^3, hence (p^3 - p^2) > p.
%F This sequence is { m : A362045(n) - m^2 < m and m in A120944 }.
%e a(1) = 42 since 42 is the smallest squarefree number such that the smallest k > m^2 such that rad(k) | m also has difference k - m^2 < m.
%e Table showing a(n) = A120944(i) = m, A362045(i) = k, and the difference k-m^2.
%e i m k (k-m^2)
%e -----------------------------
%e 14 42 1792 28
%e 22 66 4374 18
%e 27 78 6144 60
%e 147 362 131072 28
%e 478 1086 1179648 252
%e 495 1122 1259712 828
%e 558 1254 1572864 348
%e 813 1794 3219264 828
%e 822 1810 3276800 700
%e 840 1846 3407872 156
%e 900 1974 3898368 1692
%t s = Select[Range[6, 400], And[CompositeQ[#], SquareFreeQ[#]] &]; Reap[Do[(m = #^2 + 1; While[! Divisible[#, Times @@ FactorInteger[m][[All, 1]]], m++]; If[m - #^2 < #, Sow[#]]) &[s[[i]]], {i, Length[s]}] ][[-1, -1]]
%o (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
%o isok(m) = if (!isprime(m) && issquarefree(m), for (k=1+m^2, m+m^2, if (!(m % rad(k)), return(1)))); \\ _Michel Marcus_, Apr 21 2023
%Y Cf. A007947, A120944, A362045.
%K nonn
%O 1,1
%A _Michael De Vlieger_, Apr 05 2023