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

Author

Gus Wiseman, Oct 02 2019

Keywords

• nonn

Comments

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

Examples

			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.
		

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.

Programs

Mathematica

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

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).