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 A305735 #13 Feb 12 2022 20:30:54
%S A305735 0,1,1,1,1,3,1,3,2,7,1,10,1,15,8,17,1,34,1,37,16,56,1,80,6,101,27,122,
%T A305735 1,208,1,209,57,297,20,410,1,490,102,599,1,901,1,948,194,1255,1,1690,
%U A305735 14,1985,298,2337,1,3327,61,3597,491,4565,1,6031,1,6842,802
%N A305735 Number of integer partitions of n whose greatest common divisor is a prime number.
%H A305735 Andrew Howroyd, <a href="/A305735/b305735.txt">Table of n, a(n) for n = 1..1000</a>
%F A305735 a(n) = Sum_{d|n} A143519(d) * A000041(n/d). - _Andrew Howroyd_, Jun 22 2018
%e A305735 The a(10) = 7 integer partitions are (82), (64), (622), (55), (442), (4222), (22222).
%t A305735 Table[Length[Select[IntegerPartitions[n],PrimeQ[GCD@@#]&]],{n,20}]
%o A305735 (PARI) seq(n)={dirmul(vector(n, n, numbpart(n)), dirmul(vector(n, n, moebius(n)), vector(n, n, isprime(n))))} \\ _Andrew Howroyd_, Jun 22 2018
%Y A305735 Cf. A000040, A000041, A000837, A018783, A100953, A143519, A289508, A302698, A305563, A305731.
%K A305735 nonn
%O A305735 1,6
%A A305735 _Gus Wiseman_, Jun 22 2018