cp's OEIS Frontend

A328335 Numbers whose consecutive prime indices are relatively prime.

%I A328335 #7 Oct 16 2019 08:45:20
%S A328335 1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,22,23,24,26,28,29,30,
%T A328335 31,32,33,34,35,37,38,40,41,43,44,46,47,48,51,52,53,55,56,58,59,60,61,
%U A328335 62,64,66,67,68,69,70,71,73,74,76,77,79,80,82,83,85,86,88
%N A328335 Numbers whose consecutive prime indices are relatively prime.
%C A328335 First differs from A302569 in having 105, which has prime indices {2, 3, 4}.
%C A328335 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 A328335 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of partitions whose consecutive parts are relatively prime (A328172).
%e A328335 The sequence of terms together with their prime indices begins:
%e A328335    1: {}
%e A328335    2: {1}
%e A328335    3: {2}
%e A328335    4: {1,1}
%e A328335    5: {3}
%e A328335    6: {1,2}
%e A328335    7: {4}
%e A328335    8: {1,1,1}
%e A328335   10: {1,3}
%e A328335   11: {5}
%e A328335   12: {1,1,2}
%e A328335   13: {6}
%e A328335   14: {1,4}
%e A328335   15: {2,3}
%e A328335   16: {1,1,1,1}
%e A328335   17: {7}
%e A328335   19: {8}
%e A328335   20: {1,1,3}
%e A328335   22: {1,5}
%e A328335   23: {9}
%t A328335 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A328335 Select[Range[100],!MatchQ[primeMS[#],{___,x_,y_,___}/;GCD[x,y]>1]&]
%Y A328335 A superset of A302569.
%Y A328335 Numbers whose prime indices are relatively prime are A289509.
%Y A328335 Numbers with no consecutive prime indices relatively prime are A328336.
%Y A328335 Cf. A000837, A056239, A112798, A281116, A289508, A318981, A328168, A328169, A328172, A328187, A328188, A328220.
%K A328335 nonn
%O A328335 1,2
%A A328335 _Gus Wiseman_, Oct 14 2019