A002952 Smaller of unitary amicable pair. (Formerly M5372)

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

Offset

1,1

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, Nov 27 2005

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..7896 (from Pedersen's website)

Peter Hagis, Jr., Unitary amicable numbers, Math. Comp., 25 (1971), 915-918.

J. M. Pedersen, Known Unitary Amicable Pairs

J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]

J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]

J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]

Ivars Peterson, Amicable Pairs, Divisors, and a New Record, January 30 2004.

Eric Weisstein's World of Mathematics, Unitary Amicable Number.

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.

Mathematica

uDivisors[n_] := Select[Divisors[n], # < n && GCD[#, n/#] == 1 & ]; mate[n_] := If[m = Total[uDivisors[n]]; n == Total[uDivisors[m]], m, 0]; Reap[Do[If[n < mate[n], Print[n]; Sow[n]], {n, 2, 2000000}]][[2, 1]] (* Jean-François Alcover, Jun 12 2012 *)

Crossrefs

Cf. A002953, A063991, A111904.

Sequence in context: A251459 A251452 A239570 * A296403 A262416 A108344

Adjacent sequences: A002949 A002950 A002951 * A002953 A002954 A002955

Keyword

nonn,nice

Author

N. J. A. Sloane; extended Nov 24 2005

Status

approved