cp's OEIS Frontend

A307516 Numbers whose maximum prime index and minimum prime index differ by more than 1.

%I A307516 #14 Apr 12 2019 09:33:46
%S A307516 10,14,20,21,22,26,28,30,33,34,38,39,40,42,44,46,50,51,52,55,56,57,58,
%T A307516 60,62,63,65,66,68,69,70,74,76,78,80,82,84,85,86,87,88,90,91,92,93,94,
%U A307516 95,98,99,100,102,104,105,106,110,111,112,114,115,116,117,118
%N A307516 Numbers whose maximum prime index and minimum prime index differ by more than 1.
%C A307516 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. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose maximum and minimum parts differ by more than 1. The enumeration of these partitions by sum is given by A000094.
%C A307516 Differs from A069900 first at n = 43.
%e A307516 The sequence of terms together with their prime indices begins:
%e A307516    10: {1,3}
%e A307516    14: {1,4}
%e A307516    20: {1,1,3}
%e A307516    21: {2,4}
%e A307516    22: {1,5}
%e A307516    26: {1,6}
%e A307516    28: {1,1,4}
%e A307516    30: {1,2,3}
%e A307516    33: {2,5}
%e A307516    34: {1,7}
%e A307516    38: {1,8}
%e A307516    39: {2,6}
%e A307516    40: {1,1,1,3}
%e A307516    42: {1,2,4}
%e A307516    44: {1,1,5}
%e A307516    46: {1,9}
%e A307516    50: {1,3,3}
%e A307516    51: {2,7}
%e A307516    52: {1,1,6}
%e A307516    55: {3,5}
%p A307516 with(numtheory):
%p A307516 q:= n-> (l-> pi(l[-1])-pi(l[1])>1)(sort([factorset(n)[]])):
%p A307516 select(q, [$2..200])[];  # _Alois P. Heinz_, Apr 12 2019
%t A307516 Select[Range[100],PrimePi[FactorInteger[#][[-1,1]]]-PrimePi[FactorInteger[#][[1,1]]]>1&]
%Y A307516 Positions of numbers > 1 in A243055. Complement of A000961 and A256617.
%Y A307516 Cf. A000094, A000245, A001222, A052126, A056239, A061395, A064989, A069900, A105441, A112798, A307517, A325196.
%K A307516 nonn
%O A307516 1,1
%A A307516 _Gus Wiseman_, Apr 12 2019