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 A046762 Sum of the squares of the divisors of n is divisible by n. 5
 1, 10, 60, 65, 84, 130, 140, 150, 175, 260, 350, 420, 525, 780, 1050, 1105, 1820, 2100, 2210, 4420, 4650, 5425, 5460, 8840, 10500, 10850, 13260, 16275, 19720, 20150, 20737, 21700, 30225, 30940, 32045, 32550, 41474, 45500, 55250, 57350, 60450 (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[ square of divisors ]. Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006 REFERENCES Florian Luca, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113 (2006), 372-373. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 EXAMPLE n=65=a[ 4 ], sigma[ 2,65 ]=4420=65*68=68*n or n=1820=a[ 17 ], the divisor-square sum is 4641000=2550*1820=2880*n MAPLE with(numtheory); A046762:=proc(q) local a, i, n; for n from 1 to q do   a:=divisors(n); if frac(add(a[i]^2, i=1..nops(a))/n)=0 then print(n); fi; od; end: A046762(100000);  # [Paolo P. Lava, Dec 07 2012] MATHEMATICA Select[Range[70000], Divisible[DivisorSigma[2, #], #]&] [From Harvey P. Dale, Dec 15 2010] PROG (PARI) is(n)=sigma(n, 2)%n==0 \\ Charles R Greathouse IV, Feb 04 2013 CROSSREFS Sequence in context: A213346 A140890 A055714 * A066290 A065641 A121874 Adjacent sequences:  A046759 A046760 A046761 * A046763 A046764 A046765 KEYWORD nonn AUTHOR Labos E. (labos(AT)ana.sote.hu) STATUS approved

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