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A272190
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Either 6th power of a prime, or product of the square of two different primes.
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2
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36, 64, 100, 196, 225, 441, 484, 676, 729, 1089, 1156, 1225, 1444, 1521, 2116, 2601, 3025, 3249, 3364, 3844, 4225, 4761, 5476, 5929, 6724, 7225, 7396, 7569, 8281, 8649, 8836, 9025, 11236, 12321, 13225, 13924, 14161, 14884, 15129, 15625, 16641, 17689, 17956, 19881
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OFFSET
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1,1
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COMMENTS
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Numbers such that the sum of the number of divisors of their aliquot parts is three times the number of their divisors.
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LINKS
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FORMULA
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EXAMPLE
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36 = 2^2 * 3^2; 64 = 2^6.
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MAPLE
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with(numtheory): P:=proc(q) local a, k, n; for n from 2 to q do a:=sort([op(divisors(n))]);
if 3*tau(n)= add(tau(a[k]), k=1..nops(a)-1) then print(n); fi; od; end: P(10^7);
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MATHEMATICA
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Select[Range[20000], MemberQ[{{6}, {2, 2}}, FactorInteger[#][[;; , 2]]] &] (* Amiram Eldar, Oct 03 2023 *)
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PROG
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(PARI) isok(n) = 3*numdiv(n) == sumdiv(n, d, (n!=d)*numdiv(d)); \\ Michel Marcus, Apr 22 2016
(PARI) is(n) = {my(e = factor(n)[, 2]~); e == [6] || e == [2, 2]; } \\ Amiram Eldar, Oct 03 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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