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A372896
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Squarefree terms of A372894 whose prime factors are neither elite (A102742) nor anti-elite (A128852).
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1
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1, 341, 671, 1891, 2117, 3277, 4033, 5461, 8249, 12557, 13021, 14531, 19171, 24811, 31609, 32777, 33437, 40951, 46139, 48929, 49981, 50737, 73279, 80581, 84169, 100253, 116143, 130289, 135923, 136271, 149437, 175577, 179783, 194417, 252361, 272491, 342151, 343027, 376169, 390641
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OFFSET
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1,2
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COMMENTS
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By construction, A372894 is the disjoint union of the two following sets of numbers: (a) products of a square, some distinct anti-elite primes, an even number of elite-primes and a term here; (b) products of a square, some distinct anti-elite primes, an odd number of elite-primes and a term in A372895.
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LINKS
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PROG
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(PARI) isA372896(n) = {
if(n%2 && issquarefree(n) && isA372894(n), if(n==1, return(1)); my(f = factor(n)~[1, ]); \\ See A372894 for its program
for(i=1, #f, my(p=f[i], d = znorder(Mod(2, p)), StartPoint = valuation(d, 2), LengthTest = znorder(Mod(2, d >> StartPoint)), flag = 0); \\ To check if p = f[i] is an elite prime or an anti-elite prime, it suffices to check (2^2^i + 1) modulo p for StartPoint <= i <= StartPoint + LengthTest - 1; see A129802 or A372894
for(j = StartPoint+1, StartPoint + LengthTest - 1, if(issquare(Mod(2, p)^2^j + 1) != issquare(Mod(2, p)^2^StartPoint + 1), flag = 1; break())); if(flag == 0, return(0))); 1, 0)
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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