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A215926 Smallest deficient number k such that the product k*n is non-deficient (perfect or abundant). 1

%I

%S 3,2,3,4,1,4,3,2,2,8,1,8,2,2,3,16,1,16,1,2,3,16,1,4,3,2,1,16,1,16,3,2,

%T 3,2,1,32,3,2,1,32,1,32,2,2,3,32,1,4,2,2,2,32,1,4,1,2,3,32,1,32,3,2,3,

%U 4,1,64,3,2,1,64,1,64,3,2,3,4,1,64,1,2,3

%N Smallest deficient number k such that the product k*n is non-deficient (perfect or abundant).

%C If n is perfect or abundant then a(n) = 1.

%C Conjecture: a(n) is 1, 3, or a power of 2.

%C Conjecture: The first occurrence of 2^m happens at A014210(m).

%H Michel Marcus, <a href="/A215926/b215926.txt">Table of n, a(n) for n = 2..1000</a>

%e a(3) = 2 since 2*3 is perfect.

%t Table[k = 1; While[DivisorSigma[1, k] >= 2*k || DivisorSigma[1, k*n] < 2*k*n, k++]; k, {n, 2, 100}] (* _T. D. Noe_, Aug 27 2012 *)

%Y Cf. A023196, A005100.

%K nonn

%O 2,1

%A _Michel Marcus_, Aug 27 2012

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)