%I #9 Nov 13 2019 07:13:34
%S 1,2,3,5,7,9,11,13,17,19,21,23,25,27,29,31,37,39,41,43,47,49,53,57,59,
%T 61,63,65,67,71,73,79,81,83,87,89,91,97,101,103,107,109,111,113,115,
%U 117,121,125,127,129,131,133,137,139,147,149,151,157,159,163,167
%N Numbers with no consecutive prime indices relatively prime.
%C First differs from A318978 in having 897, with prime indices {2, 6, 9}.
%C 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 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 no consecutive parts relatively prime (A328187).
%C Besides the initial 1 this differs from A305078: 47541=897*prime(16) is in A305078 but not in this set. - _Andrey Zabolotskiy_, Nov 13 2019
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 3: {2}
%e 5: {3}
%e 7: {4}
%e 9: {2,2}
%e 11: {5}
%e 13: {6}
%e 17: {7}
%e 19: {8}
%e 21: {2,4}
%e 23: {9}
%e 25: {3,3}
%e 27: {2,2,2}
%e 29: {10}
%e 31: {11}
%e 37: {12}
%e 39: {2,6}
%e 41: {13}
%e 43: {14}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],!MatchQ[primeMS[#],{___,x_,y_,___}/;GCD[x,y]==1]&]
%Y Numbers with consecutive prime indices relatively prime are A328335.
%Y Strict partitions with no consecutive parts relatively prime are A328220.
%Y Numbers with relatively prime prime indices are A289509.
%Y Cf. A000837, A056239, A078374, A112798, A281116, A289508, A318981, A328168, A328169, A328172, A328187, A328188.
%K nonn
%O 1,2
%A _Gus Wiseman_, Oct 14 2019