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A325778 Heinz numbers of integer partitions whose distinct consecutive subsequences have different sums. 11
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
First differs from A299702 in having 462.
The enumeration of these partitions by sum is given by A325769.
LINKS
EXAMPLE
Most small numbers are in the sequence. However, the sequence of non-terms together with their prime indices begins:
12: {1,1,2}
24: {1,1,1,2}
30: {1,2,3}
36: {1,1,2,2}
40: {1,1,1,3}
48: {1,1,1,1,2}
60: {1,1,2,3}
63: {2,2,4}
70: {1,3,4}
72: {1,1,1,2,2}
80: {1,1,1,1,3}
84: {1,1,2,4}
90: {1,2,2,3}
96: {1,1,1,1,1,2}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], UnsameQ@@Total/@Union[ReplaceList[primeMS[#], {___, s__, ___}:>{s}]]&]
CROSSREFS
Complement of A325777.
Sequence in context: A085235 A364461 A160453 * A364531 A299702 A348577
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 20 2019
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)