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%I #5 Feb 12 2021 17:51:44
%S 12,20,56,88,104,272,304,368,464,992,1184,1312,1376,1504,1696,1888,
%T 1952,4288,4544,4672,5056,5312,5696,6208,6464,6592,6848,6976,7232,
%U 16256,16768,17536,17792,19072,19328,20096,20864,21376,22144,22912,23168,24448
%N a(n) is the smallest abundant number of the form 2^e * prime(n).
%C Note that the sum of divisors of 2^e * p for an odd prime p is (2^(e+1)-1) * (p+1).
%F Let p = prime(n), then a(n) = p * 2^floor(log_2(p+1)). Also a(n) = p * 2^floor(log_2(p)) is p is not a Mersenne prime (A000668), p * 2^(floor(log_2(p))+1) otherwise.
%F a(n) ~ prime(n)^2.
%e For p = prime(4) = 7, 2^0 * 7 = 7, 2^1 * 7 = 14 are both deficient, 2^2 * 7 = 28 is perfect and 2^3 * 7 = 56 is abundant. Hence a(4) = 56.
%o (PARI) a(n) = my(p=prime(n)); p << logint(p+1, 2)
%Y Cf. A005101, A000668.
%K nonn,easy
%O 2,1
%A _Jianing Song_, Feb 09 2021
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