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

1, 2, 3, 6, 7, 13, 20, 29, 37, 39, 42, 53, 61, 79, 107, 110, 113, 151, 173, 181, 199, 239, 261, 271, 281, 312, 317, 349, 359, 374, 397, 421, 457, 497, 503, 541, 557, 577, 593, 613, 701, 733, 769, 787, 798, 857, 863, 903, 911, 953, 983, 1021, 1061, 1069, 1151

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..55.

Example

The sequence of terms together with their prime indices begins:
     1: {}
     2: {1}
     3: {2}
     6: {1,2}
     7: {4}
    13: {6}
    20: {1,1,3}
    29: {10}
    37: {12}
    39: {2,6}
    42: {1,2,4}
    53: {16}
    61: {18}
    79: {22}
   107: {28}
   110: {1,3,5}
   113: {30}
   151: {36}
   173: {40}
   181: {42}
   199: {46}
   239: {52}
   261: {2,2,10}
   271: {58}
   281: {60}
   312: {1,1,1,2,6}
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.

Mathematica

nn=1000;
Select[Union[Table[Times@@Prime/@Differences[Divisors[n]], {n, nn}]], #<=nn&]

Crossrefs

A permutation of A328023.

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

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

Sequence in context: A328164 A294916 A233423 * A309815 A256800 A172105

Adjacent sequences: A328021 A328022 A328023 * A328025 A328026 A328027

Keyword

nonn

Author

Gus Wiseman, Oct 02 2019

Status

approved