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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. 4

%I

%S 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 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 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 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 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%C This sequence is idempotent, meaning a(a(n)) = a(n) for all n.

%C All terms belong to A289509.

%H Antti Karttunen, <a href="/A316437/b316437.txt">Table of n, a(n) for n = 1..65537</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Idempotence">Idempotence</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%t f[n_]:=If[n==1,1,With[{pms=Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]},Times@@Prime/@(pms/GCD@@pms)]];

%t Table[f[n],{n,100}]

%o (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 Cf. A000720, A056239, A289508, A289509, A290103, A296150, A316430, A316431, A316432, A316438.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jul 03 2018

%E More terms from _Antti Karttunen_, Aug 06 2018

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)