cp's OEIS Frontend

A381077 Sorted positions of first appearances in A380986 (product of prime indices minus product of distinct prime indices).

%I A381077 #5 Feb 22 2025 09:56:39
%S A381077 1,9,25,49,63,81,99,121,125,135,169,171,245,279,289,343,361,363,369,
%T A381077 375,387,477,529,531,575,603,625,675,711,729,747,833,841,847,873,875,
%U A381077 891,909,961,981,1029,1083,1125,1127,1179,1225,1251,1377,1413,1445,1467
%N A381077 Sorted positions of first appearances in A380986 (product of prime indices minus product of distinct prime indices).
%C A381077 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. A position of first appearance in a sequence q is an index k such that q(k) is different from q(j) for all j < k.
%C A381077 All terms are odd.
%e A381077 The terms together with their prime indices begin:
%e A381077      1: {}
%e A381077      9: {2,2}
%e A381077     25: {3,3}
%e A381077     49: {4,4}
%e A381077     63: {2,2,4}
%e A381077     81: {2,2,2,2}
%e A381077     99: {2,2,5}
%e A381077    121: {5,5}
%e A381077    125: {3,3,3}
%e A381077    135: {2,2,2,3}
%e A381077    169: {6,6}
%e A381077    171: {2,2,8}
%e A381077    245: {3,4,4}
%e A381077    279: {2,2,11}
%t A381077 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A381077 q=Table[Times@@prix[n]-Times@@Union[prix[n]],{n,10000}];
%t A381077 Select[Range[Length[q]],FreeQ[Take[q,#-1],q[[#]]]&]
%Y A381077 For length instead of product we have A151821, firsts of A046660.
%Y A381077 For factors instead of indices we have A381076, sorted firsts of A066503.
%Y A381077 For sum of factors instead of product of indices we have A381075 (unsorted A280286), A280292.
%Y A381077 For quotient instead of difference we have A380988 (unsorted A380987), firsts of A290106.
%Y A381077 For quotient and factors we have A001694 (unsorted A064549), firsts of A003557.
%Y A381077 For sum instead of product we have A380957 (unsorted A380956), firsts of A380955.
%Y A381077 Sorted firsts of A380986, which has nonzero terms at positions A038838.
%Y A381077 A000040 lists the primes, differences A001223.
%Y A381077 A003963 gives product of prime indices, distinct A156061.
%Y A381077 A005117 lists the squarefree numbers, complement A013929.
%Y A381077 A007947 gives squarefree kernel.
%Y A381077 A055396 gives least prime index, greatest A061395.
%Y A381077 A056239 adds up prime indices, row sums of A112798, length A001222.
%Y A381077 A304038 lists distinct prime indices, sum A066328, length A001221.
%Y A381077 Cf. A000079, A000720, A001222, A081770, A075255, A116861, A178503, A374248, A379681, A380958.
%K A381077 nonn
%O A381077 1,2
%A A381077 _Gus Wiseman_, Feb 20 2025