This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A316430 #13 Jul 25 2024 14:04:46
%S A316430 1,2,9,21,39,57,87,91,111,125,129,159,183,203,213,237,247,267,301,303,
%T A316430 321,325,339,377,393,417,427,453,489,519,543,551,553,559,575,579,597,
%U A316430 669,687,689,707,717,753,789,791,813,817,843,845,879,923,925,933,951,973
%N A316430 Heinz numbers of integer partitions whose length is equal to the GCD of all the parts.
%C A316430 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A316430 2 is the only even term in the sequence. 3k is in the sequence if and only if k is in A031215. 5k is in the sequence if and only if k = pq with p and q in A031336.
%F A316430 a(n) << n log^2 n, can this be improved? - _Charles R Greathouse IV_, Jul 25 2024
%e A316430 Sequence of integer partitions whose length is equal to their GCD begins: (), (1), (2,2), (4,2), (6,2), (8,2), (10,2), (6,4), (12,2), (3,3,3), (14,2), (16,2), (18,2), (10,4), (20,2), (22,2), (8,6), (24,2), (14,4), (26,2), (28,2), (6,3,3).
%t A316430 Select[Range[200],PrimeOmega[#]==GCD@@Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]]&]
%o A316430 (PARI) is(n,f=factor(n))=gcd(apply(primepi,f[,1]))==vecsum(f[,2]) \\ _Charles R Greathouse IV_, Jul 25 2024
%Y A316430 Subsequence of A004280.
%Y A316430 Cf. A056239, A067538, A074761, A143773, A289508, A289509, A296150, A316413, A316431, A316432, A316433, A031215, A031336.
%K A316430 nonn
%O A316430 1,2
%A A316430 _Gus Wiseman_, Jul 02 2018