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A048768 Numbers n such that A048767(n) = n.

%I A048768 #23 Oct 21 2023 01:49:56
%S A048768 1,2,9,12,18,40,112,125,250,352,360,675,832,1008,1125,1350,1500,2176,
%T A048768 2250,2401,3168,3969,4802,4864,7488,7938,11776,14000,19584,21609,
%U A048768 28812,29403,29696,43218,43776,44000,58806,63488,75600,96040,104000,105984,123201,126000
%N A048768 Numbers n such that A048767(n) = n.
%C A048768 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions that are fixed points under the map described in A217605 (which interchanges the parts with their multiplicities). The enumeration of these partitions by sum is given by A217605. - _Gus Wiseman_, May 04 2019
%H A048768 Amiram Eldar, <a href="/A048768/b048768.txt">Table of n, a(n) for n = 1..128</a>
%e A048768 12 = (2^2)*(3^1) = (2nd prime)^pi(2) * (first prime)^pi(3).
%e A048768 From _Gus Wiseman_, May 04 2019: (Start)
%e A048768 The sequence of terms together with their prime indices begins:
%e A048768      1: {}
%e A048768      2: {1}
%e A048768      9: {2,2}
%e A048768     12: {1,1,2}
%e A048768     18: {1,2,2}
%e A048768     40: {1,1,1,3}
%e A048768    112: {1,1,1,1,4}
%e A048768    125: {3,3,3}
%e A048768    250: {1,3,3,3}
%e A048768    352: {1,1,1,1,1,5}
%e A048768    360: {1,1,1,2,2,3}
%e A048768    675: {2,2,2,3,3}
%e A048768    832: {1,1,1,1,1,1,6}
%e A048768   1008: {1,1,1,1,2,2,4}
%e A048768   1125: {2,2,3,3,3}
%e A048768   1350: {1,2,2,2,3,3}
%e A048768   1500: {1,1,2,3,3,3}
%e A048768   2176: {1,1,1,1,1,1,1,7}
%e A048768   2250: {1,2,2,3,3,3}
%e A048768   2401: {4,4,4,4}
%e A048768 (End)
%t A048768 wt[n_]:=Times@@Cases[FactorInteger[n],{p_,k_}:>Prime[k]^PrimePi[p]];
%t A048768 Select[Range[1000],wt[#]==#&] (* _Gus Wiseman_, May 04 2019 *)
%o A048768 (PARI) is(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); #Set(e) == #e && prod(i = 1, #e, prime(e[i])^primepi(p[i])) == n;} \\ _Amiram Eldar_, Oct 20 2023
%Y A048768 A subsequence of A130091.
%Y A048768 Cf. A008478, A048767, A048769, A056239, A098859, A109297, A109298, A112798, A118914, A217605, A325326, A325368.
%K A048768 nonn,eigen
%O A048768 1,2
%A A048768 _Naohiro Nomoto_
%E A048768 a(1) inserted and more terms added by _Amiram Eldar_, Oct 20 2023