A254603 Nonprime numbers n such that sum of the divisors of n is a power of 2.

1, 21, 93, 217, 381, 651, 889, 2667, 3937, 11811, 24573, 27559, 57337, 82677, 172011, 253921, 393213, 761763, 917497, 1040257, 1572861, 1777447, 2752491, 3120771, 3670009, 4063201, 5332341, 7281799, 11010027, 12189603, 16252897, 16646017, 21845397, 28442407

Offset

1,2

Comments

a(1)=1; for n>=2, a(n) = composite numbers that are a product of distinct Mersenne primes (A046528).

Also nonprime numbers n such that A051027(n) = sigma(sigma(n)) = 2*sigma(n)-1 = 2^(k+1)-1 for some k. If n is composite number (product of distinct Mersenne primes) then k is the sum of Mersenne exponents (A000043) of these distinct Mersenne primes. Example: 651 = 3*7*31 = (2^2-1)*(2^3-1)*(2^5-1); k=2+3+5=10; A051027(651) = sigma(sigma(651)) = 2^(10+1)-1 = 2047.

Complement of A000668 (Mersenne primes) with respect to A046528.

Links

Table of n, a(n) for n=1..34.

Example

651 = 3*7*31 (product of three distinct Mersenne primes); sigma(651) = 1024 = 2^10.

Prog

(Magma) [n: n in [1..10^6] | not IsPrime(n) and SumOfDivisors(SumOfDivisors(n)) eq 2*SumOfDivisors(n) - 1]
(Magma)[n: n in[1..10000], k in [0..100] | not IsPrime(n) and SumOfDivisors(n) eq 2^k]

Crossrefs

Cf. A000043, A000203, A000668, A046528, A051027.

Sequence in context: A326164 A143843 A119109 * A144856 A065522 A218844

Adjacent sequences: A254600 A254601 A254602 * A254604 A254605 A254606

Keyword

nonn

Author

Jaroslav Krizek, Feb 02 2015

Status

approved