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A002952
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Smaller of unitary amicable pair.
(Formerly M5372)
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5
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114, 1140, 18018, 32130, 44772, 56430, 67158, 142310, 180180, 197340, 241110, 296010, 308220, 462330, 591030, 669900, 671580, 785148, 815100, 1004850, 1077890, 1080150, 1156870, 1177722, 1222650, 1281540, 1475810, 1511930, 1571388
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| I proved the following facts: (a) If (m,n) is a unitary amicable pair such that mod(m,4)= mod(n,4)=2 and 5 doesn't divide m*n then (10*m,10*n) is a unitary amicable pair. (b) If (m,n) is a unitary amicable pair such that m/12 and n/12 are natural numbers and gcd(m/12,12)=gcd(n/12,12)=1 then (3/2*m,3/2*n) is a unitary amicable pair. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Nov 27 2005
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REFERENCES
| P. Hagis, Jr., Unitary amicable numbers, Math. Comp., 25 (1971), 915-918.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..7896 (from Pedersen's website)
I. Peterson, Math Trek
J. M. Pedersen, Known Unitary Amicable Pairs
J. O. M. Pedersen, Tables of Aliquot Cycles
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
| (114,126) is a unitary amicable pair: 114 has unitary divisors 1, (2,57), (3,38) and (6,19), apart from 114 itself. Their sum is 126, whose unitary divisors < 126 are 1, (2,63), (7,18), (9,14) whose sum is 114.
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CROSSREFS
| Cf. A002953, A063991, A111904.
Sequence in context: A122279 A126169 A174072 * A108344 A200551 A200891
Adjacent sequences: A002949 A002950 A002951 * A002953 A002954 A002955
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com); extended Nov 24 2005
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