login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259037 Non-unitary amicable numbers. 3
48, 56, 192, 248, 252, 328, 448, 496, 768, 1016, 1792, 2032, 3240, 6462, 7936, 8128, 11616, 11808, 17412, 20538, 49152, 65528, 114688, 131056, 507904, 524224, 786432, 1048568, 1835008, 2080768, 2096896, 2097136, 3145728, 4194296, 7340032, 8126464, 8388544, 8388592, 32505856, 33292288, 33554176, 33554368, 133169152, 134217472 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A pair of integers x and y is called non-unitary amicable if the sum of the non-unitary divisors of either one is equal to the other. Union of A259038 and A259039.

The sequence lists the non-unitary amicable numbers in increasing order. Note that the pairs x, y are not always adjacent to each other in the list. See also A259038 for the x's, A259039 for the y's. The first time a pair is not adjacent is x = 11616, y = 17412 which correspond to a(17) and a(19), respectively.

No other pair below 10^9.

Ligh & Wall showed that if p and q are different Mersenne exponents (A000043) (i.e., 2^p - 1 and 2^q - 1 are Mersenne primes), then 2^(p+1) * (2^q-1) and 2^(q+1) * (2^p-1) is a nonunitary amicable pair. They also found the pairs (252, 328), (3240, 6462), (11616, 17412), (11808, 20538), which are all the known pairs that are not based on Mersenne primes. - Amiram Eldar, Sep 27 2018

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..48

Steve Ligh and Charles R. Wall, Functions of Nonunitary Divisors, Fibonacci Quarterly, Vol. 25 (1987), pp. 333-338.

Eric Weisstein's World of Mathematics, Unitary Divisor Function

Wikipedia, Unitary divisor

EXAMPLE

48 and 56 are in the sequence, as sigma(48)-usigma(48) = 56 and sigma(56)-usigma(56) = 48.

PROG

(PARI) A048146(n)=my(f=factor(n)); sigma(f)-prod(i=1, #f~, f[i, 1]^f[i, 2]+1)

is(n)=my(k=A048146(n)); k>1 && k!=n && A048146(k)==n \\ Charles R Greathouse IV, Jun 17 2015

CROSSREFS

Subsequence of A013929.

Cf. A000043, A034448, A048146, A259038, A259039.

Sequence in context: A080854 A255267 A345503 * A231469 A261546 A335938

Adjacent sequences:  A259034 A259035 A259036 * A259038 A259039 A259040

KEYWORD

nonn

AUTHOR

Mauro Fiorentini, Jun 17 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 11:47 EST 2022. Contains 358359 sequences. (Running on oeis4.)