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%I #43 Nov 01 2023 08:46:11
%S 1,16,32,64,81,128,243,256,512,625,729,1024,1296,2048,2187,2401,2592,
%T 3125,3888,4096,5184,6561,7776,8192,10000,10368,11664,14641,15552,
%U 15625,16384,16807,19683,20000,20736,23328,28561,31104,32768,34992
%N 4-full numbers: if a prime p divides k then so does p^4.
%C a(m) mod prime(n) > 0 for m < A258601(n); a(A258601(n)) = A030514(n) = prime(n)^4. - _Reinhard Zumkeller_, Jun 06 2015
%D E. Kraetzel, Lattice Points, Kluwer, Chap. 7, p. 276.
%H Alois P. Heinz, <a href="/A036967/b036967.txt">Table of n, a(n) for n = 1..10000</a> (first 300 terms from T. D. Noe)
%F Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p^3*(p-1))) = 1.1488462139214317030108176090790939019972506733993367867997411290952527... - _Amiram Eldar_, Jul 09 2020
%t Join[{1},Select[Range[35000],Min[Transpose[FactorInteger[#]][[2]]]>3&]] (* _Harvey P. Dale_, Jun 05 2012 *)
%o (Haskell)
%o import Data.Set (singleton, deleteFindMin, fromList, union)
%o a036967 n = a036967_list !! (n-1)
%o a036967_list = 1 : f (singleton z) [1, z] zs where
%o f s q4s p4s'@(p4:p4s)
%o | m < p4 = m : f (union (fromList $ map (* m) ps) s') q4s p4s'
%o | otherwise = f (union (fromList $ map (* p4) q4s) s) (p4:q4s) p4s
%o where ps = a027748_row m
%o (m, s') = deleteFindMin s
%o (z:zs) = a030514_list
%o -- _Reinhard Zumkeller_, Jun 03 2015
%o (PARI) is(n)=n==1 || vecmin(factor(n)[,2])>3 \\ _Charles R Greathouse IV_, Sep 17 2015
%o (Python)
%o from sympy import factorint
%o A036967_list = [n for n in range(1,10**5) if min(factorint(n).values(),default=4) >= 4] # _Chai Wah Wu_, Aug 18 2021
%Y A030514 is a subsequence.
%Y Cf. A001694, A036966, A046101, A258601.
%K easy,nonn,nice
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Erich Friedman_
%E Corrected by _Vladeta Jovovic_, Aug 17 2002
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