A325779 Heinz numbers of integer partitions for which every restriction to a subinterval has a different sum.

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107

Offset

1,2

Comments

First differs from A301899 in having 462.

The enumeration of these partitions by sum is given by A325768.

Links

Table of n, a(n) for n=1..65.

Example

Most small numbers are in the sequence. However, the sequence of non-terms together with their prime indices begins:
    4: {1,1}
    8: {1,1,1}
    9: {2,2}
   12: {1,1,2}
   16: {1,1,1,1}
   18: {1,2,2}
   20: {1,1,3}
   24: {1,1,1,2}
   25: {3,3}
   27: {2,2,2}
   28: {1,1,4}
   30: {1,2,3}
   32: {1,1,1,1,1}
   36: {1,1,2,2}
   40: {1,1,1,3}
   44: {1,1,5}
   45: {2,2,3}
   48: {1,1,1,1,2}
   49: {4,4}
   50: {1,3,3}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], UnsameQ@@ReplaceList[primeMS[#], {___, s__, ___}:>Plus[s]]&]

Crossrefs

A subsequence of A005117.

Cf. A000041, A002033, A056239, A103300, A112798, A143823, A169942, A299702, A301899, A325676, A325768, A325769, A325770, A325778.

Sequence in context: A284892 A319315 A325467 * A301899 A325398 A325399

Adjacent sequences: A325776 A325777 A325778 * A325780 A325781 A325782

Keyword

nonn

Author

Gus Wiseman, May 20 2019

Status

approved