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A356657
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Numbers k that can be written as the sum of 8 divisors of k (not necessarily distinct).
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9
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8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 76, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 136, 138, 140, 144, 150, 152, 154, 156, 160, 162, 168, 170, 174, 176
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OFFSET
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1,1
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COMMENTS
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Terms are even. Proof by contradiction. Suppose m = a(n) is odd. Then each divisor is odd. Adding 8 odd numbers gives an even number. A contradiction. - David A. Corneth, Sep 02 2022
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LINKS
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EXAMPLE
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14 is in the sequence since 14 = 2+2+2+2+2+2+1+1, where each summand divides 14.
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PROG
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(PARI) isok(k) = my(d=divisors(k)); forpart(p=k, if (setintersect(d, Set(p)) == Set(p), return(1)), , [8, 8]); \\ Michel Marcus, Aug 21 2022
(PARI) is(n) = if(n % 2 == 1, return(0)); my(d = divisors(n)); forvec(x = vector(8, i, [1, #d-1]), s=sum(i=1, #x, d [x[i]]); if(n == s, print(vector(#x, j, d[x[j]])); return(1)), 1); 0 \\ David A. Corneth, Aug 21 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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