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

1, 4, 8, 16, 18, 20, 24, 25, 27, 32, 44, 48, 50, 52, 54, 64, 68, 72, 75, 76, 80, 81, 92, 96, 98, 108, 112, 116, 121, 125, 128, 144, 148, 152, 160, 162, 164, 172, 175, 176, 188, 189, 192, 196, 198, 200, 212, 216, 232, 236, 242, 243, 244, 256, 260, 264, 268, 272

Offset: 1

Author

Gus Wiseman, Feb 18 2025

Keywords

• nonn

Comments

In A066503, each value appears for the first time at one of these positions.

Crossrefs

For quotient instead of difference we have A001694, sorted firsts of A003557.

Sorted positions of first appearances in A066503.

For indices and sum we have A380957 (unsorted A380956), firsts of A380955.

For indices and quotient we have A380988 (unsorted A380987), firsts of A290106.

For sum instead of product we have A381075, sorted firsts of A280292, see A280286.

For indices instead of factors we have A381077, sorted firsts of A380986.

A000040 lists the primes, differences A001223.

A001414 adds up prime factors (indices A056239), row sums of A027746 (indices A112798).

A003963 gives product of prime indices, distinct A156061.

A005117 lists squarefree numbers, complement A013929.

A007947 gives squarefree kernel.

A020639 gives least prime factor (index A055396), greatest A061395 (index A006530).

Cf. A001221, A001222, A038838, A046660, A075255, A081770, A116861, A136565, A178503, A175508, A304038, A380989.

Programs

Mathematica

prifacs[n_]:=If[n==1,{},Flatten[Apply[ConstantArray,FactorInteger[n],{1}]]];
q=Table[Times@@prifacs[n]-Times@@Union[prifacs[n]],{n,1000}];
Select[Range[Length[q]],FreeQ[Take[q,#-1],q[[#]]]&]