cp's OEIS Frontend

A328168 Numbers whose prime indices minus 1 are relatively prime.

%I A328168 #6 Oct 13 2019 07:37:50
%S A328168 3,6,9,12,15,18,21,24,27,30,33,35,36,39,42,45,48,51,54,57,60,63,65,66,
%T A328168 69,70,72,75,77,78,81,84,87,90,91,93,95,96,99,102,105,108,111,114,117,
%U A328168 120,123,126,129,130,132,133,135,138,140,141,143,144,145,147
%N A328168 Numbers whose prime indices minus 1 are relatively prime.
%C A328168 A multiset is relatively prime if the GCD of its elements is 1. Zeros are ignored when computing GCD, and the empty set has GCD 0.
%C A328168 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 A328168 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 parts minus one are relatively prime. The enumeration of these partitions by sum is given by A328170.
%e A328168 The sequence of terms together with their prime indices begins:
%e A328168     3: {2}
%e A328168     6: {1,2}
%e A328168     9: {2,2}
%e A328168    12: {1,1,2}
%e A328168    15: {2,3}
%e A328168    18: {1,2,2}
%e A328168    21: {2,4}
%e A328168    24: {1,1,1,2}
%e A328168    27: {2,2,2}
%e A328168    30: {1,2,3}
%e A328168    33: {2,5}
%e A328168    35: {3,4}
%e A328168    36: {1,1,2,2}
%e A328168    39: {2,6}
%e A328168    42: {1,2,4}
%e A328168    45: {2,2,3}
%e A328168    48: {1,1,1,1,2}
%e A328168    51: {2,7}
%e A328168    54: {1,2,2,2}
%e A328168    57: {2,8}
%p A328168 q:= n-> igcd(map(i-> numtheory[pi](i[1])-1, ifactors(n)[2])[])=1:
%p A328168 select(q, [$1..150])[];  # _Alois P. Heinz_, Oct 13 2019
%t A328168 Select[Range[100],GCD@@(PrimePi/@First/@If[#==1,{},FactorInteger[#]]-1)==1&]
%Y A328168 Positions of 1's in A328167.
%Y A328168 Numbers whose prime indices are relatively prime are A289509.
%Y A328168 The version for prime indices plus 1 is A318981.
%Y A328168 The GCD of prime indices is A289508.
%Y A328168 Partitions whose parts minus 1 are relatively prime are A328170.
%Y A328168 Cf. A000837, A056239, A112798, A258409, A281116, A290103, A328163, A328169.
%K A328168 nonn
%O A328168 1,1
%A A328168 _Gus Wiseman_, Oct 08 2019