cp's OEIS Frontend

A328674 Numbers whose distinct prime indices have no consecutive divisible parts.

%I A328674 #7 Nov 01 2019 18:40:40
%S A328674 1,2,3,4,5,7,8,9,11,13,15,16,17,19,23,25,27,29,31,32,33,35,37,41,43,
%T A328674 45,47,49,51,53,55,59,61,64,67,69,71,73,75,77,79,81,83,85,89,91,93,95,
%U A328674 97,99,101,103,105,107,109,113,119,121,123,125,127,128,131,135
%N A328674 Numbers whose distinct prime indices have no consecutive divisible parts.
%C A328674 First differs from A316476 in having 105, with prime indices {2, 3, 4}.
%C A328674 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 A328674 The sequence of terms together with their prime indices begins:
%e A328674     1: {}
%e A328674     2: {1}
%e A328674     3: {2}
%e A328674     4: {1,1}
%e A328674     5: {3}
%e A328674     7: {4}
%e A328674     8: {1,1,1}
%e A328674     9: {2,2}
%e A328674    11: {5}
%e A328674    13: {6}
%e A328674    15: {2,3}
%e A328674    16: {1,1,1,1}
%e A328674    17: {7}
%e A328674    19: {8}
%e A328674    23: {9}
%e A328674    25: {3,3}
%e A328674    27: {2,2,2}
%e A328674    29: {10}
%e A328674    31: {11}
%e A328674    32: {1,1,1,1,1}
%e A328674 For example, 45 is in the sequence because its distinct prime indices are {2,3} and 2 is not a divisor of 3.
%t A328674 Select[Range[100],!MatchQ[PrimePi/@First/@FactorInteger[#],{___,x_,y_,___}/;Divisible[y,x]]&]
%Y A328674 These are the Heinz numbers of the partitions counted by A328675.
%Y A328674 The strict version is A328603.
%Y A328674 Partitions without consecutive divisibilities are A328171.
%Y A328674 Compositions without consecutive divisibilities are A328460.
%Y A328674 Cf. A056239, A112798, A316476, A318729, A328335, A328336, A328593, A328598.
%K A328674 nonn
%O A328674 1,2
%A A328674 _Gus Wiseman_, Oct 29 2019