cp's OEIS Frontend

A335241 Numbers whose prime indices are not pairwise coprime, where a singleton is not coprime unless it is {1}.

%I A335241 #8 May 30 2020 19:14:37
%S A335241 1,3,5,7,9,11,13,17,18,19,21,23,25,27,29,31,36,37,39,41,42,43,45,47,
%T A335241 49,50,53,54,57,59,61,63,65,67,71,72,73,75,78,79,81,83,84,87,89,90,91,
%U A335241 97,98,99,100,101,103,105,107,108,109,111,113,114,115,117,121
%N A335241 Numbers whose prime indices are not pairwise coprime, where a singleton is not coprime unless it is {1}.
%C A335241 We use the Mathematica definition for CoprimeQ, so a singleton is not considered coprime unless it is (1).
%C A335241 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.
%e A335241 The sequence of terms together with their prime indices begins:
%e A335241     1: {}          31: {11}          61: {18}
%e A335241     3: {2}         36: {1,1,2,2}     63: {2,2,4}
%e A335241     5: {3}         37: {12}          65: {3,6}
%e A335241     7: {4}         39: {2,6}         67: {19}
%e A335241     9: {2,2}       41: {13}          71: {20}
%e A335241    11: {5}         42: {1,2,4}       72: {1,1,1,2,2}
%e A335241    13: {6}         43: {14}          73: {21}
%e A335241    17: {7}         45: {2,2,3}       75: {2,3,3}
%e A335241    18: {1,2,2}     47: {15}          78: {1,2,6}
%e A335241    19: {8}         49: {4,4}         79: {22}
%e A335241    21: {2,4}       50: {1,3,3}       81: {2,2,2,2}
%e A335241    23: {9}         53: {16}          83: {23}
%e A335241    25: {3,3}       54: {1,2,2,2}     84: {1,1,2,4}
%e A335241    27: {2,2,2}     57: {2,8}         87: {2,10}
%e A335241    29: {10}        59: {17}          89: {24}
%t A335241 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335241 Select[Range[100],!CoprimeQ@@primeMS[#]&]
%Y A335241 The complement is A302696.
%Y A335241 The version for relatively prime instead of coprime is A318978.
%Y A335241 The version for standard compositions is A335239.
%Y A335241 These are the Heinz numbers of the partitions counted by A335240.
%Y A335241 Singleton or pairwise coprime partitions are counted by A051424.
%Y A335241 Singleton or pairwise coprime sets are ranked by A087087.
%Y A335241 Primes and numbers with pairwise coprime prime indices are A302569.
%Y A335241 Numbers whose binary indices are pairwise coprime are A326675.
%Y A335241 Coprime standard composition numbers are A333227.
%Y A335241 Cf. A007360, A101268, A326674, A327516, A333228, A335236, A335237, A335238.
%K A335241 nonn
%O A335241 1,2
%A A335241 _Gus Wiseman_, May 30 2020