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Composite terms in A376471.
2

%I #7 Sep 24 2024 09:28:55

%S 6,9,20,25,77,81,121,208,256,323,361,625,667,841,1147,1369,1763,1849,

%T 2303,2401,3127,3481,4087,4489,5183,5329,6557,6561,6889,8633,9409,

%U 10403,10609,11663,11881,14351,14641,16129,17947,18769,20711,22201,23707,24649,27221

%N Composite terms in A376471.

%C Are there terms in this sequence that have more than 2 distinct prime factors?

%H Amiram Eldar, <a href="/A376472/b376472.txt">Table of n, a(n) for n = 1..204</a>

%t expPow2Q[n_] := AllTrue[FactorInteger[n][[;; , 2]], # == 2^IntegerExponent[#, 2] &]; s[1] = 1; s[n_] := s[n] = Module[{prod = Times @@ Array[s, n - 1], k = s[n - 1] + 1}, While[! expPow2Q[prod*k], k++]; k]; Select[Array[s, 1000], CompositeQ]

%o (PARI) ispow2(n) = if(n == 0, 1, n >> valuation(n, 2) == 1);

%o lista(pindmax) = {my(pmax = prime(pindmax), v = vector(pindmax), f, pind, prd); for(k = 2, pmax, f = factor(k); pind = apply(x -> primepi(x), f[,1]); for(i = 1, #pind, v[pind[i]] += f[i, 2]); if(vecprod(apply(x -> ispow2(x), v)) > 0, if(!isprime(k), print1(k, ", ")), for(i = 1, #pind, v[pind[i]] -= f[i, 2])));}

%Y Intersection of A002808 and A376471.

%K nonn

%O 1,1

%A _Amiram Eldar_, Sep 24 2024