A328023 Heinz number of the multiset of differences between consecutive divisors of n.

1, 2, 3, 6, 7, 20, 13, 42, 39, 110, 29, 312, 37, 374, 261, 798, 53, 2300, 61, 3828, 903, 1426, 79, 18648, 497, 2542, 2379, 21930, 107, 86856, 113, 42294, 4503, 5546, 2247, 475800, 151, 7906, 8787, 370620, 173, 843880, 181, 249798, 92547, 12118, 199, 5965848

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..48.

Formula

A056239(a(n)) = n - 1. In words, the integer partition with Heinz number a(n) is an integer partition of n - 1.

A055396(a(n)) = A060680(n).

A061395(a(n)) = A060681(n).

A001221(a(n)) = A060682(n).

A001222(a(n)) = A000005(n).

Example

The sequence of terms together with their prime indices begins:
            1: ()
            2: (1)
            3: (2)
            6: (2,1)
            7: (4)
           20: (3,1,1)
           13: (6)
           42: (4,2,1)
           39: (6,2)
          110: (5,3,1)
           29: (10)
          312: (6,2,1,1,1)
           37: (12)
          374: (7,5,1)
          261: (10,2,2)
          798: (8,4,2,1)
           53: (16)
         2300: (9,3,3,1,1)
           61: (18)
         3828: (10,5,2,1,1)
For example, the divisors of 6 are {1,2,3,6}, with differences {1,1,3}, with Heinz number 20, so a(6) = 20.

Mathematica

Table[Times@@Prime/@Differences[Divisors[n]], {n, 100}]

Crossrefs

The sorted version is A328024.

a(n) is the Heinz number of row n of A193829, A328025, or A328027.

Cf. A000005, A027750, A056239, A060682, A060683, A112798, A129308, A193829.

Sequence in context: A079663 A064622 A119746 * A265481 A023785 A050581

Adjacent sequences: A328020 A328021 A328022 * A328024 A328025 A328026

Keyword

nonn

Author

Gus Wiseman, Oct 02 2019

Status

approved