A328024 - OEIS

%I #6 Oct 03 2019 08:39:40

%S 1,2,3,6,7,13,20,29,37,39,42,53,61,79,107,110,113,151,173,181,199,239,

%T 261,271,281,312,317,349,359,374,397,421,457,497,503,541,557,577,593,

%U 613,701,733,769,787,798,857,863,903,911,953,983,1021,1061,1069,1151

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

%C The Heinz number of an integer partition or multiset {y_1,...,y_k} is prime(y_1)*...*prime(y_k).

%C There is exactly one entry with any given sum of prime indices A056239.

%e The sequence of terms together with their prime indices begins:

%e      1: {}

%e      2: {1}

%e      3: {2}

%e      6: {1,2}

%e      7: {4}

%e     13: {6}

%e     20: {1,1,3}

%e     29: {10}

%e     37: {12}

%e     39: {2,6}

%e     42: {1,2,4}

%e     53: {16}

%e     61: {18}

%e     79: {22}

%e    107: {28}

%e    110: {1,3,5}

%e    113: {30}

%e    151: {36}

%e    173: {40}

%e    181: {42}

%e    199: {46}

%e    239: {52}

%e    261: {2,2,10}

%e    271: {58}

%e    281: {60}

%e    312: {1,1,1,2,6}

%e 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 nn=1000;

%t Select[Union[Table[Times@@Prime/@Differences[Divisors[n]],{n,nn}]],#<=nn&]

%Y A permutation of A328023.

%Y Also the set of possible Heinz numbers of rows of A193829, A328025, or A328027.

%Y Cf. A001222, A000005, A027750, A056239, A060680, A060681, A060682, A112798.

%K nonn

%O 1,2

%A _Gus Wiseman_, Oct 02 2019