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A381076 Sorted positions of first appearances in A066503 (n minus squarefree kernel of n).

%I A381076 #7 Feb 19 2025 22:12:01
%S A381076 1,4,8,16,18,20,24,25,27,32,44,48,50,52,54,64,68,72,75,76,80,81,92,96,
%T A381076 98,108,112,116,121,125,128,144,148,152,160,162,164,172,175,176,188,
%U A381076 189,192,196,198,200,212,216,232,236,242,243,244,256,260,264,268,272
%N A381076 Sorted positions of first appearances in A066503 (n minus squarefree kernel of n).
%C A381076 In A066503, each value appears for the first time at one of these positions.
%t A381076 prifacs[n_]:=If[n==1,{},Flatten[Apply[ConstantArray,FactorInteger[n],{1}]]];
%t A381076 q=Table[Times@@prifacs[n]-Times@@Union[prifacs[n]],{n,1000}];
%t A381076 Select[Range[Length[q]],FreeQ[Take[q,#-1],q[[#]]]&]
%Y A381076 For quotient instead of difference we have A001694, sorted firsts of A003557.
%Y A381076 Sorted positions of first appearances in A066503.
%Y A381076 For indices and sum we have A380957 (unsorted A380956), firsts of A380955.
%Y A381076 For indices and quotient we have A380988 (unsorted A380987), firsts of A290106.
%Y A381076 For sum instead of product we have A381075, sorted firsts of A280292, see A280286.
%Y A381076 For indices instead of factors we have A381077, sorted firsts of A380986.
%Y A381076 A000040 lists the primes, differences A001223.
%Y A381076 A001414 adds up prime factors (indices A056239), row sums of A027746 (indices A112798).
%Y A381076 A003963 gives product of prime indices, distinct A156061.
%Y A381076 A005117 lists squarefree numbers, complement A013929.
%Y A381076 A007947 gives squarefree kernel.
%Y A381076 A020639 gives least prime factor (index A055396), greatest A061395 (index A006530).
%Y A381076 Cf. A001221, A001222, A038838, A046660, A075255, A081770, A116861, A136565, A178503, A175508, A304038, A380989.
%K A381076 nonn
%O A381076 1,2
%A A381076 _Gus Wiseman_, Feb 18 2025