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A351119
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Numbers that are the sum of two balanced numbers in at least one way.
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0
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2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 20, 21, 24, 26, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 41, 42, 43, 44, 45, 47, 48, 49, 50, 54, 56, 57, 58, 59, 60, 62, 65, 68, 70, 71, 72, 73, 76, 77, 79, 80, 81, 82, 84, 85, 86, 90, 91, 92, 93, 98, 100, 105, 106, 107, 108
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OFFSET
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1,1
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COMMENTS
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A balanced number k is a number such that phi(k) | sigma(k).
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LINKS
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EXAMPLE
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8 is in the sequence since the balanced numbers less than 8 are: 1, 2, 3, 6 and 6 + 2 = 8.
10 is not in the sequence since the balanced numbers less than 10 are: 1, 2, 3, 6, and no two sum to 10.
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MATHEMATICA
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m = 100; balanced = Select[Range[m], Divisible[DivisorSigma[1, #], EulerPhi[#]] &]; q[n_] := Length[IntegerPartitions[n, {2}, balanced]] > 0; Select[Range[m], q] (* Amiram Eldar, Feb 01 2022 *)
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PROG
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(PARI) isb(n) = (sigma(n) % eulerphi(n)) == 0;
isok(m) = for (k=1, m-1, if (isb(k) && isb(m-k), return(1))); \\ Michel Marcus, Feb 01 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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