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A254603 Nonprime numbers n such that sum of the divisors of n is a power of 2. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 23:53 EDT 2020. Contains 336280 sequences. (Running on oeis4.)