A341361 a(n) is the smallest abundant number of the form 2^e * prime(n).

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

Table of n, a(n) for n=2..43.

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.

Prog

(PARI) a(n) = my(p=prime(n)); p << logint(p+1, 2)

Crossrefs

Cf. A005101, A000668.

Sequence in context: A229355 A259174 A109788 * A181701 A025104 A163323

Adjacent sequences: A341358 A341359 A341360 * A341362 A341363 A341364

Keyword

nonn,easy

Author

Jianing Song, Feb 09 2021

Status

approved