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A046839
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Numbers k such that the number of divisors of k divides the sum of cubes of divisors of k.
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2
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1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102, 103
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OFFSET
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1,2
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COMMENTS
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The first 42 terms agree with A003601 but a(43)=64 is not present in A003601.
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LINKS
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EXAMPLE
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a(43) = 64. The sigma(k,64) values for k=0,1,2,3 are as follows: 7, 127, 5461 and 299593. While 7 does not divide the sum of divisors, 127, it divides the sum of d^3 values: Sum(d^3) = 299593 = 7*127*337.
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MATHEMATICA
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Select[Range[103], Divisible[DivisorSigma[3, #], DivisorSigma[0, #]] &] (* _Jayanta Basu_, Jun 29 2013 *)
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PROG
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(Magma) [n: n in [1..110] | IsZero(DivisorSigma(3, n) mod NumberOfDivisors(n))]; // _Bruno Berselli_, Apr 11 2013
(PARI) isok(n) = sigma(n, 3) % numdiv(n) == 0; \\ _Michel Marcus_, May 13 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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_Labos Elemer_
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STATUS
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approved
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