cp's OEIS Frontend

A328024 Heinz numbers of multisets representing the differences between some positive integer's consecutive divisors.

%I A328024 #6 Oct 03 2019 08:39:40
%S A328024 1,2,3,6,7,13,20,29,37,39,42,53,61,79,107,110,113,151,173,181,199,239,
%T A328024 261,271,281,312,317,349,359,374,397,421,457,497,503,541,557,577,593,
%U A328024 613,701,733,769,787,798,857,863,903,911,953,983,1021,1061,1069,1151
%N A328024 Heinz numbers of multisets representing the differences between some positive integer's consecutive divisors.
%C A328024 The Heinz number of an integer partition or multiset {y_1,...,y_k} is prime(y_1)*...*prime(y_k).
%C A328024 There is exactly one entry with any given sum of prime indices A056239.
%e A328024 The sequence of terms together with their prime indices begins:
%e A328024      1: {}
%e A328024      2: {1}
%e A328024      3: {2}
%e A328024      6: {1,2}
%e A328024      7: {4}
%e A328024     13: {6}
%e A328024     20: {1,1,3}
%e A328024     29: {10}
%e A328024     37: {12}
%e A328024     39: {2,6}
%e A328024     42: {1,2,4}
%e A328024     53: {16}
%e A328024     61: {18}
%e A328024     79: {22}
%e A328024    107: {28}
%e A328024    110: {1,3,5}
%e A328024    113: {30}
%e A328024    151: {36}
%e A328024    173: {40}
%e A328024    181: {42}
%e A328024    199: {46}
%e A328024    239: {52}
%e A328024    261: {2,2,10}
%e A328024    271: {58}
%e A328024    281: {60}
%e A328024    312: {1,1,1,2,6}
%e A328024 For example, the divisors of 8 are {1,2,4,8}, with differences {1,2,4}, with Heinz number 42, so 42 belongs to the sequence.
%t A328024 nn=1000;
%t A328024 Select[Union[Table[Times@@Prime/@Differences[Divisors[n]],{n,nn}]],#<=nn&]
%Y A328024 A permutation of A328023.
%Y A328024 Also the set of possible Heinz numbers of rows of A193829, A328025, or A328027.
%Y A328024 Cf. A001222, A000005, A027750, A056239, A060680, A060681, A060682, A112798.
%K A328024 nonn
%O A328024 1,2
%A A328024 _Gus Wiseman_, Oct 02 2019