A066505 f-amicable numbers where f(n) = n+1.

36, 62, 168, 326, 9936, 14056, 16198, 19862, 45304, 51910, 82662, 90152, 337688, 388102, 472902, 479672, 1970586, 2353756, 2969288, 3769942, 6319544, 8454886, 12276056, 13125574, 16783976, 17948854, 18818780, 20825882, 21738114, 22479040, 25960468, 31470614

Offset: 1

Author

Joseph L. Pe, Jan 04 2002

Keywords

• nonn

Comments

f-amicable pairs are defined similarly to f-perfect numbers in A066218. That is, a, b is a f-amicable pair if f(a) = D(b) and f(b) = D(a), where D(n) = sum_{k divides n, k

Pairs are (36,62), (14056,16198), (9936,19862), (45304,51910), (82662,90152) (337688,388102) and (472902,479672). The sequence shows them unbundled, then elements sorted according to size. - R. J. Mathar, Sep 07 2006, Dec 07 2006

Examples

			Proper divisors of 36 = {1, 2, 3, 4, 6, 9, 12, 18}. f applied to these divisors = {2, 3, 4, 5, 7, 10, 13, 19}; their sum = 63. So D(36) = f(62). proper divisors of 62 = {1, 2, 31}. f applied to these divisors = {2, 3, 32}; their sum = 37. So D(62) = f(36). Therefore 36, 62 is an f-amicable pair.
		

Links

• J. L. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.

Crossrefs

Cf. A066229, A066218.

Programs

Mathematica

f[x_] := x + 1; d[x_] := Apply[ Plus, Map[ f, Divisors[ x] ] ] - f[ x]; m = Table[{x, y}, {x, 1, 1000}, {y, 1, 1000}]; Do[a = m[[i, j]]; If[ (a[[1]] < a[[2]]) && (f[a[[1]]] == d[a[[2]]]) && (f[a[[2]]] == d[a[[1]]]), Print[{i, j}]], {i, 1, 1000}, {j, 1, 1000}]

Extensions

More terms from John W. Layman, Nov 11 2002

More terms from R. J. Mathar, Sep 07 2006

a(17)-a(32) from Donovan Johnson, Jun 23 2012

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