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A283486 Number of k such that sigma(k) = 2n where sigma(m) = A000203(m) is the sum of the divisors of m. 2

%I #15 Feb 22 2020 20:54:24

%S 0,1,1,1,0,2,1,0,2,1,0,3,0,1,1,2,0,1,1,1,3,1,0,3,0,0,2,2,0,3,1,0,0,1,

%T 0,5,1,0,1,2,0,3,0,0,3,0,0,4,2,0,1,2,0,2,1,1,2,0,0,4,0,2,2,2,0,2,0,0,

%U 1,2,0,5,0,0,1,2,0,2,1,1,1,1,0,6,0,0,1,1,0,4,2,0,2,0,0,5

%N Number of k such that sigma(k) = 2n where sigma(m) = A000203(m) is the sum of the divisors of m.

%C First occurrence of k: 1, 2, 6, 12, 48, 36, 84, ...

%H Charles R Greathouse IV, <a href="/A283486/b283486.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A054973(2n) - _Michel Marcus_, Mar 08 2017.

%e a(12) = 3 because sigma(14) = 1 + 2 + 7 + 14 = 24, sigma(15) = 1 + 3 + 5 + 15 = 24 and sigma(23) = 1 + 23 = 24.

%o (PARI) first(n)=my(v=vector(n),t);for(k=1,2*n-1, t=sigma(k)/2; if(t<=n && denominator(t)==1, v[t]++)); v \\ _Charles R Greathouse IV_, Mar 08 2017

%Y Cf. A000203, A054973, A060658.

%K nonn

%O 1,6

%A _Juri-Stepan Gerasimov_, Mar 08 2017

%E a(96) corrected by _Charles R Greathouse IV_, Mar 08 2017

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)