cp's OEIS Frontend

A328336 Numbers with no consecutive prime indices relatively prime.

%I A328336 #9 Nov 13 2019 07:13:34
%S A328336 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 A328336 61,63,65,67,71,73,79,81,83,87,89,91,97,101,103,107,109,111,113,115,
%U A328336 117,121,125,127,129,131,133,137,139,147,149,151,157,159,163,167
%N A328336 Numbers with no consecutive prime indices relatively prime.
%C A328336 First differs from A318978 in having 897, with prime indices {2, 6, 9}.
%C A328336 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 A328336 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 A328336 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 A328336 The sequence of terms together with their prime indices begins:
%e A328336    1: {}
%e A328336    2: {1}
%e A328336    3: {2}
%e A328336    5: {3}
%e A328336    7: {4}
%e A328336    9: {2,2}
%e A328336   11: {5}
%e A328336   13: {6}
%e A328336   17: {7}
%e A328336   19: {8}
%e A328336   21: {2,4}
%e A328336   23: {9}
%e A328336   25: {3,3}
%e A328336   27: {2,2,2}
%e A328336   29: {10}
%e A328336   31: {11}
%e A328336   37: {12}
%e A328336   39: {2,6}
%e A328336   41: {13}
%e A328336   43: {14}
%t A328336 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A328336 Select[Range[100],!MatchQ[primeMS[#],{___,x_,y_,___}/;GCD[x,y]==1]&]
%Y A328336 Numbers with consecutive prime indices relatively prime are A328335.
%Y A328336 Strict partitions with no consecutive parts relatively prime are A328220.
%Y A328336 Numbers with relatively prime prime indices are A289509.
%Y A328336 Cf. A000837, A056239, A078374, A112798, A281116, A289508, A318981, A328168, A328169, A328172, A328187, A328188.
%K A328336 nonn
%O A328336 1,2
%A A328336 _Gus Wiseman_, Oct 14 2019