cp's OEIS Frontend

A316437 Take the integer partition with Heinz number n, divide all parts by the GCD of the parts, then take the Heinz number of the resulting partition.

%I A316437 #10 Aug 26 2018 12:24:17
%S A316437 1,2,2,4,2,6,2,8,4,10,2,12,2,14,15,16,2,18,2,20,6,22,2,24,4,26,8,28,2,
%T A316437 30,2,32,33,34,35,36,2,38,10,40,2,42,2,44,45,46,2,48,4,50,51,52,2,54,
%U A316437 55,56,14,58,2,60,2,62,12,64,6,66,2,68,69,70,2,72,2,74,75,76,77,78,2,80,16,82,2,84,85,86,22,88,2,90,15
%N A316437 Take the integer partition with Heinz number n, divide all parts by the GCD of the parts, then take the Heinz number of the resulting partition.
%C A316437 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A316437 This sequence is idempotent, meaning a(a(n)) = a(n) for all n.
%C A316437 All terms belong to A289509.
%H A316437 Antti Karttunen, <a href="/A316437/b316437.txt">Table of n, a(n) for n = 1..65537</a>
%H A316437 Wikipedia, <a href="https://en.wikipedia.org/wiki/Idempotence">Idempotence</a>
%H A316437 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%t A316437 f[n_]:=If[n==1,1,With[{pms=Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]},Times@@Prime/@(pms/GCD@@pms)]];
%t A316437 Table[f[n],{n,100}]
%o A316437 (PARI) A316437(n) = if(1==n,1,my(f = factor(n), pis = apply(p -> primepi(p), f[, 1]~), es = f[, 2]~, g = gcd(pis)); factorback(vector(#f~, k, prime(pis[k]/g)^es[k]))); \\ _Antti Karttunen_, Aug 06 2018
%Y A316437 Cf. A000720, A056239, A289508, A289509, A290103, A296150, A316430, A316431, A316432, A316438.
%K A316437 nonn
%O A316437 1,2
%A A316437 _Gus Wiseman_, Jul 03 2018
%E A316437 More terms from _Antti Karttunen_, Aug 06 2018