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 A046763 Numbers n such that the sum of the cubes of the divisors of n is divisible by n. 5
 1, 6, 42, 120, 168, 270, 280, 312, 496, 672, 728, 840, 1080, 1560, 1782, 1806, 1890, 2044, 2184, 2520, 3472, 3640, 3913, 4256, 5880, 6048, 6552, 6615, 7224, 7560, 7826, 8128, 9120, 9424, 9933, 10804, 10920, 11400, 12040, 12768, 13230, 13626, 14040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Compare with multiply perfect numbers, A007691. Here Sum[ divisors ] is replaced by Sum[ cube of divisors ]. Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006 Tomohiro Yamada found that the odd number 209195 is a member. (See the Editorial Comment after the solution to Problem 11090.) - Jonathan Sondow, Nov 23 2012 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe) Florian Luca and John Ferdinands, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113:4 (2006), pp. 372-373. EXAMPLE n = 168 = a[ 5 ], Sum[ d^3 ] = 5634720 = 33540*168 = 33540*n or if n = 8128, Sigma[ 3,8128 ] = 613681507712 = 8128*75502154. Moreover 8128 is a perfect number. MAPLE with(numtheory); A046763:=proc(q) local a, i, n; for n from 1 to q do   a:=divisors(n); if frac(add(a[i]^3, i=1..nops(a))/n)=0 then print(n); fi; od; end: A046763(100000);  # Paolo P. Lava, Dec 07 2012 MATHEMATICA Select[Range[10^4], Divisible[DivisorSigma[3, #], #] &] (* Amiram Eldar, Sep 10 2019 *) PROG (PARI) is(n)=sigma(n, 3)%n==0 \\ Charles R Greathouse IV, Feb 04 2013 CROSSREFS Cf. A001158, A007691. Sequence in context: A256833 A164016 A147811 * A199905 A176780 A169938 Adjacent sequences:  A046760 A046761 A046762 * A046764 A046765 A046766 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 14 12:45 EDT 2019. Contains 328006 sequences. (Running on oeis4.)