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Smallest prime factor of n-th partition number.
3

%I #18 Feb 16 2025 08:32:51

%S 1,2,3,5,7,11,3,2,2,2,2,7,101,3,2,3,3,5,2,3,2,2,5,3,2,2,2,2,5,2,2,3,3,

%T 2,3,17977,7,5,3,2,3,2,3,5,2,2,2,3,5,2,3,3,3,5,2,11,2,2,2,17,3,2,3,2,

%U 2,2,1181,3,5,2,3,11,23,2,2,7,10619863,2,2,2,11,5,7,2,11,2,11,3,5,2473

%N Smallest prime factor of n-th partition number.

%H Giovanni Resta, <a href="/A087173/b087173.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LeastPrimeFactor.html">Least Prime Factor</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunction.html">Partition Function</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>

%F a(n) = A020639(A000041(n)).

%e A000041(100) = 190569292 = 2*2*43*59*89*211, therefore a(100)=2.

%t FactorInteger[#][[1,1]]&/@PartitionsP[Range[90]] (* _Harvey P. Dale_, May 20 2023 *)

%o (PARI) spf(n) = if (n==1, 1, vecmin(factor(n)[,1]));

%o a(n) = spf(numbpart(n)); \\ _Michel Marcus_, Feb 24 2023

%Y Cf. A071963.

%K nonn,changed

%O 1,2

%A _Reinhard Zumkeller_, Aug 23 2003