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Search: id:A002952
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| A002952 |
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Smaller of unitary amicable pair.
(Formerly M5372)
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+0
4
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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; listen)
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OFFSET
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1,1
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COMMENT
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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 (f.firoozbakht(AT)math.ui.ac.ir), Nov 27 2005
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REFERENCES
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P. Hagis, Jr., Unitary amicable numbers, Math. Comp., 25 (1971), 915-918.
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LINKS
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J. M. Pedersen, Known Unitary Amicable Pairs
I. Peterson, Math Trek
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
J. O. M. Pedersen, Tables of Aliquot Cycles
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EXAMPLE
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(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
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Cf. A002953, A063991, A111904.
Adjacent sequences: A002949 A002950 A002951 this_sequence A002953 A002954 A002955
Sequence in context: A043403 A122279 A126169 this_sequence A108344 A112485 A084877
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com); extended Nov 24 2005
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