cp's OEIS Frontend

A318991 Numbers whose consecutive prime indices are divisible. Heinz numbers of integer partitions in which each part is divisible by the next.

%I A318991 #9 Oct 27 2018 01:08:00
%S A318991 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,
%T A318991 28,29,31,32,34,36,37,38,39,40,41,42,43,44,46,47,48,49,50,52,53,54,56,
%U A318991 57,58,59,61,62,63,64,65,67,68,71,72,73,74,76,78,79,80
%N A318991 Numbers whose consecutive prime indices are divisible. Heinz numbers of integer partitions in which each part is divisible by the next.
%C A318991 A prime index of n is a number m such that prime(m) divides n.
%C A318991 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A318991 Andrew Howroyd, <a href="/A318991/b318991.txt">Table of n, a(n) for n = 1..10000</a>
%e A318991 The sequence of all dividing partitions (columns) begins:
%e A318991    1  2  1  3  2  4  1  2  3  5  2  6  4  1  7  2  8  3  4  5  9  2  3  6  2  4
%e A318991          1     1     1  2  1     1     1  1     2     1  2  1     1  3  1  2  1
%e A318991                      1           1        1     1     1           1        2  1
%e A318991                                           1                       1
%t A318991 Select[Range[100],Or[#==1,PrimePowerQ[#],Divisible@@Reverse[PrimePi/@FactorInteger[#][[All,1]]]]&]
%o A318991 (PARI) ok(n)={my(v=apply(primepi, factor(n)[,1])); for(i=2, #v, if(v[i]%v[i-1], return(0))); 1} \\ _Andrew Howroyd_, Oct 26 2018
%Y A318991 Cf. A000040, A001221, A001222, A003238, A008480, A300912, A318990, A318992, A318993.
%K A318991 nonn
%O A318991 1,2
%A A318991 _Gus Wiseman_, Sep 06 2018