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 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: A255267 A366250 A345503 * A231469 A261546 A335938 Adjacent sequences: A259034 A259035 A259036 * A259038 A259039 A259040 KEYWORD nonn AUTHOR Mauro Fiorentini, Jun 17 2015 STATUS approved

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Last modified August 6 18:55 EDT 2024. Contains 374981 sequences. (Running on oeis4.)