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A336354
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Numbers k such that p^2 divides k, where p = A006530(k), the largest prime factor of k, and sigma(k) does not have any prime factor larger than p.
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2
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343, 686, 1029, 1372, 1715, 2058, 2744, 3430, 4116, 4489, 5145, 6241, 6860, 8232, 8978, 9261, 10290, 10976, 12482, 13467, 13720, 17956, 18522, 18723, 18769, 20580, 22201, 22445, 24964, 26569, 26934, 31205, 31423, 32761, 32928, 35912, 36481, 37044, 37446, 37538, 40401
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OFFSET
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1,1
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LINKS
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EXAMPLE
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343 = 7^3 is present, as A000203(343) = 400 = 2^4 * 5^2, with none of the prime factors > 7.
1715 = 5 * 7^3 is present, as sigma(1715) = 2400 = 2^5 * 3 * 5^2.
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PROG
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(PARI) is(n) = {if(n == 1, return(0));
my(f = factor(n), s, fs);
if(f[#f~, 2] < 2, return(0));
s = sigma(f);
fs = factor(s, f[#f~, 1]);
fs[#fs~, 1] <= f[#f~, 1]
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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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