A325706 Heinz numbers of integer partitions containing all of their distinct multiplicities.

1, 2, 6, 9, 10, 12, 14, 18, 22, 26, 30, 34, 36, 38, 40, 42, 46, 58, 60, 62, 66, 70, 74, 78, 82, 84, 86, 90, 94, 102, 106, 110, 112, 114, 118, 120, 122, 125, 126, 130, 132, 134, 138, 142, 146, 150, 154, 156, 158, 166, 170, 174, 178, 180, 182, 186, 190, 194, 198

Offset

1,2

Comments

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

Also numbers n divisible by the squarefree kernel of their "shadow" A181819(n).

The enumeration of these partitions by sum is given by A325705.

Links

Table of n, a(n) for n=1..59.

Example

The sequence of terms together with their prime indices begins:
    1: {}
    2: {1}
    6: {1,2}
    9: {2,2}
   10: {1,3}
   12: {1,1,2}
   14: {1,4}
   18: {1,2,2}
   22: {1,5}
   26: {1,6}
   30: {1,2,3}
   34: {1,7}
   36: {1,1,2,2}
   38: {1,8}
   40: {1,1,1,3}
   42: {1,2,4}
   46: {1,9}
   58: {1,10}
   60: {1,1,2,3}
   62: {1,11}

Mathematica

Select[Range[100], #==1||SubsetQ[PrimePi/@First/@FactorInteger[#], Last/@FactorInteger[#]]&]

Crossrefs

Cf. A056239, A109297, A112798, A114639, A114640, A181819, A225486, A290689, A324753, A324843, A325702, A325705, A325707, A325755.

Sequence in context: A121248 A268677 A108370 * A367683 A325185 A285532

Adjacent sequences: A325703 A325704 A325705 * A325707 A325708 A325709

Keyword

nonn

Author

Gus Wiseman, May 18 2019

Status

approved