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A307547 a(n) is the smallest divisor of the partition number P(n) = A000041(n) not already in the sequence.

%I A307547 #18 Jul 29 2019 17:00:12
%S A307547 1,2,3,5,7,11,15,22,6,14,4,77,101,9,8,21,27,35,10,19,12,167,251,25,89,
%T A307547 28,43,13,55,467,311,23,49,1231,33,17977,281,121,45,42,193,2417,71,31,
%U A307547 41,73,38,7013,275,9283,363,53,63,17,142,47,102359,20,44,139
%N A307547 a(n) is the smallest divisor of the partition number P(n) = A000041(n) not already in the sequence.
%C A307547 Provided A046641(m) is defined for any number m > 0, this sequence is a permutation of the natural numbers.
%H A307547 Rémy Sigrist, <a href="/A307547/b307547.txt">Table of n, a(n) for n = 1..5000</a>
%H A307547 Rémy Sigrist, <a href="/A307547/a307547.gp.txt">PARI program for A307547</a>
%F A307547 a(A049575(k)) = A049575(k).
%e A307547 The first terms, alongside the divisors of P(n), are:
%e A307547   n   a(n)  div(P(n))
%e A307547   --  ----  --------------------
%e A307547    1     1  (1)
%e A307547    2     2  (1, 2)
%e A307547    3     3  (1, 3)
%e A307547    4     5  (1, 5)
%e A307547    5     7  (1, 7)
%e A307547    6    11  (1, 11)
%e A307547    7    15  (1, 3, 5, 15)
%e A307547    8    22  (1, 2, 11, 22)
%e A307547    9     6  (1, 2, 3, 5, 6, 10, 15, 30)
%e A307547   10    14  (1, 2, 3, 6, 7, 14, 21, 42)
%o A307547 (PARI) See Links section.
%Y A307547 Cf. A000041, A046641, A049575, A309200.
%K A307547 nonn
%O A307547 1,2
%A A307547 _Rémy Sigrist_, Jul 27 2019