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A110178 Composite numbers n such that the equation sigma(n)=sigma(k)+sigma(n-k) has no solution, where sigma is the sum of divisors function. 1
4, 6, 12, 14, 16, 18, 22, 24, 25, 26, 27, 28, 34, 35, 36, 38, 42, 44, 45, 46, 48, 50, 52, 54, 58, 60, 64, 65, 66, 68, 72, 74, 76, 77, 78, 80, 81, 82, 84, 86, 91, 95, 98, 100, 102, 106, 112, 115, 118, 119, 120, 121, 122, 124, 132, 133, 138, 142, 143, 144, 146, 148, 154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The only prime for which this equation has a solution is 3.

LINKS

Table of n, a(n) for n=1..63.

MATHEMATICA

a[n_] := Select[Range[n-1], DivisorSigma[1, n]==DivisorSigma[1, n-# ]+DivisorSigma[1, # ]&]; t=Table[Length[a[n]], {n, 200}]; Complement[Flatten[Position[t, 0]], Prime[Range[PrimePi[200]]]]

CROSSREFS

Sequence in context: A310595 A175593 A163097 * A318712 A140599 A282280

Adjacent sequences:  A110175 A110176 A110177 * A110179 A110180 A110181

KEYWORD

nonn

AUTHOR

T. D. Noe, Jul 15 2005

STATUS

approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)