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A341361
a(n) is the smallest abundant number of the form 2^e * prime(n).
1
12, 20, 56, 88, 104, 272, 304, 368, 464, 992, 1184, 1312, 1376, 1504, 1696, 1888, 1952, 4288, 4544, 4672, 5056, 5312, 5696, 6208, 6464, 6592, 6848, 6976, 7232, 16256, 16768, 17536, 17792, 19072, 19328, 20096, 20864, 21376, 22144, 22912, 23168, 24448
OFFSET
2,1
COMMENTS
Note that the sum of divisors of 2^e * p for an odd prime p is (2^(e+1)-1) * (p+1).
LINKS
FORMULA
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.
a(n) ~ prime(n)^2.
EXAMPLE
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.
MATHEMATICA
a[n_] := Module[{p = Prime[n]}, p * 2^Floor[Log2[p+1]]]; Array[a, 100, 2] (* Amiram Eldar, Jul 25 2024 *)
PROG
(PARI) a(n) = my(p=prime(n)); p << logint(p+1, 2)
CROSSREFS
Sequence in context: A229355 A259174 A109788 * A181701 A025104 A163323
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Feb 09 2021
STATUS
approved