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A328023
Heinz number of the multiset of differences between consecutive divisors of n.
5
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).
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.
Sequence in context: A079663 A064622 A119746 * A265481 A023785 A050581
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 02 2019
STATUS
approved