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Numbers in A093891, but not A005153.
2

%I #7 Mar 06 2021 06:25:26

%S 10,70,350,490,572,770,836,910,1190,1330,1430,1610,1750,1870,2030,

%T 2090,2170,2210,2470,2530,2584,2590,2750,2870,2990,3010,3128,3190,

%U 3230,3250,3290,3410,3430,3710,3850,3944,4130,4216,4270,4550,4690,5032,5390,5576

%N Numbers in A093891, but not A005153.

%C A number n is in this sequence if the sums of distinct divisors of n form all the primes up to sigma(n), but do not form all the integers up to sigma(n).

%H Amiram Eldar, <a href="/A174434/b174434.txt">Table of n, a(n) for n = 1..2000</a>

%t Test[n_] := Module[{d=Divisors[n],t,lim,x}, t=CoefficientList[Product[1+x^i, {i,d}],x]; lim=PrimePi[Length[t]-1]; Count[t[[1+Prime[Range[lim]]]], _?(#>0&)] == lim && Count[t,0] > 0]; Select[Range[1000], Test]

%Y Cf. A005153, A093891.

%K nonn

%O 1,1

%A _T. D. Noe_, Mar 19 2010