cp's OEIS Frontend

A380987 Position of first appearance of n in A290106 (product of prime indices divided by product of distinct prime indices).

%I A380987 #8 Feb 18 2025 15:34:09
%S A380987 1,9,25,27,121,169,289,81,125,841,961,675,1681,1849,2209,243,3481,
%T A380987 1125,4489,3267,5329,6241,6889,2025,1331,10201,625,7803,11881,12769,
%U A380987 16129,729,18769,19321,22201,2197,24649,26569,27889,9801,32041,32761,36481,25947
%N A380987 Position of first appearance of n in A290106 (product of prime indices divided by product of distinct prime indices).
%C A380987 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A380987 All terms are odd.
%e A380987 The first position of 12 in A290106 is 675, with prime indices {2,2,2,3,3}, so a(12) = 675.
%e A380987 The terms together with their prime indices begin:
%e A380987       1: {}
%e A380987       9: {2,2}
%e A380987      25: {3,3}
%e A380987      27: {2,2,2}
%e A380987     121: {5,5}
%e A380987     169: {6,6}
%e A380987     289: {7,7}
%e A380987      81: {2,2,2,2}
%e A380987     125: {3,3,3}
%e A380987     841: {10,10}
%e A380987     961: {11,11}
%e A380987     675: {2,2,2,3,3}
%e A380987    1681: {13,13}
%e A380987    1849: {14,14}
%e A380987    2209: {15,15}
%e A380987     243: {2,2,2,2,2}
%e A380987    3481: {17,17}
%e A380987    1125: {2,2,3,3,3}
%t A380987 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A380987 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A380987 q=Table[Times@@prix[n]/Times@@Union[prix[n]],{n,10000}];
%t A380987 Table[Position[q,k][[1,1]],{k,mnrm[q]}]
%Y A380987 For factors instead of indices we have A064549 (sorted A001694), firsts of A003557.
%Y A380987 The additive version for factors is A280286 (sorted A381075), firsts of A280292.
%Y A380987 Position of first appearance of n in A290106.
%Y A380987 The additive version is A380956 (sorted A380957), firsts of A380955.
%Y A380987 For difference instead of quotient see A380986.
%Y A380987 The sorted version is A380988.
%Y A380987 A000040 lists the primes, differences A001223.
%Y A380987 A003963 gives product of prime indices, distinct A156061.
%Y A380987 A005117 lists squarefree numbers, complement A013929.
%Y A380987 A055396 gives least prime index, greatest A061395.
%Y A380987 A056239 adds up prime indices, row sums of A112798, length A001222.
%Y A380987 A304038 lists distinct prime indices, sum A066328, length A001221.
%Y A380987 Cf. A000720, A007947, A046660, A066503, A071625, A136565, A178503, A175508, A325034, A379681.
%K A380987 nonn
%O A380987 1,2
%A A380987 _Gus Wiseman_, Feb 14 2025