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%I #20 Sep 25 2019 10:43:54
%S 2,60,120,180,504,720,11550,12180,17940,19380,21252,22230,26334,27846,
%T 29172,32340,34440,34580,43470,48840,56430,59220,59670,63240,66120,
%U 70686,82824,85140,91350,95700,95940,99528,112840,113220,113652,115368
%N Numbers whose number of divisors equals the sum of their separate prime-power decompositions.
%D S. Kahan, "Divisor Advisory", Journal of Recreational Mathematics 30(1) 41-4 1999-2000 Baywood NY.
%H Amiram Eldar, <a href="/A087004/b087004.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Donovan Johnson)
%e 504 = 2^3*3^2*7 is in the sequence because d(504) = A000005(504) = (3+1)*(2+1)*(1+1) = 24 = 2^3 + 3^2 + 7. Similarly for 32340 = 2^2*3*5*7^2*11, where d(32340) = 2^2 + 3 + 5 + 7^2 + 11 = 72.
%t ndppdQ[n_]:=DivisorSigma[0,n]==Total[#[[1]]^#[[2]]&/@FactorInteger[n]]; Select[Range[2,120000],ndppdQ] (* _Harvey P. Dale_, Nov 22 2013 *)
%o (PARI) isok(n) = my(f = factor(n)); numdiv(n) == sum(i=1, #f~, f[i,1]^f[i,2]); \\ _Michel Marcus_, Oct 26 2013
%Y Cf. A078511.
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Oct 13 2003
%E a(1) = 2 prepended by _Michel Marcus_, Oct 26 2013