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Smallest prime factors of 4-full numbers, a(1)=1.
6

%I #27 Sep 09 2024 02:41:21

%S 1,2,2,2,3,2,3,2,2,5,3,2,2,2,3,7,2,5,2,2,2,3,2,2,2,2,2,11,2,5,2,7,3,2,

%T 2,2,13,2,2,2,2,2,2,2,2,3,3,2,2,2,2,5,2,2,17,2,2,2,7,2,19,2,2,3,2,2,

%U 11,2,3,2,3,2,2,2,2,2,3,2,2,23,2,2,2,2

%N Smallest prime factors of 4-full numbers, a(1)=1.

%H Reinhard Zumkeller, <a href="/A258569/b258569.txt">Table of n, a(n) for n = 1..10000</a> (some terms corrected by Georg Fischer)

%F a(n) = A020639(A036967(n));

%F a(A258601(n)) = A000040(n) and a(m) != A000040(n) for m < A258601(n).

%t Reap[Sow[1]; Do[f = FactorInteger[k]; If[Min[f[[All, 2]]] >= 4, Sow[f[[1, 1]]]], {k, 2, 10^6}]][[2, 1]] (* _Jean-François Alcover_, Sep 29 2020 *)

%o (Haskell)

%o a258569 = a020639 . a036967

%o (PARI) lista(kmax) = {my(f); print1(1, ", "); for(k = 2, kmax, f = factor(k); if(vecmin(f[, 2]) > 3, print1(f[1, 1], ", ")));} \\ _Amiram Eldar_, Sep 09 2024

%Y Cf. A036967, A020639, A258601, A258567, A258568, A258570, A258571.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jun 06 2015