A325233 Heinz numbers of integer partitions with Dyson rank 1.

3, 10, 15, 25, 28, 42, 63, 70, 88, 98, 105, 132, 147, 175, 198, 208, 220, 245, 297, 308, 312, 330, 343, 462, 468, 484, 495, 520, 544, 550, 693, 702, 726, 728, 770, 780, 816, 825, 1053, 1078, 1089, 1092, 1144, 1155, 1170, 1210, 1216, 1224, 1300, 1352, 1360

Offset

1,1

Comments

Numbers whose maximum prime index is one greater than their number of prime indices counted with multiplicity.

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

Links

Table of n, a(n) for n=1..51.

FindStat, St000145: The Dyson rank of a partition

Example

The sequence of terms together with their prime indices begins:
     3: {2}
    10: {1,3}
    15: {2,3}
    25: {3,3}
    28: {1,1,4}
    42: {1,2,4}
    63: {2,2,4}
    70: {1,3,4}
    88: {1,1,1,5}
    98: {1,4,4}
   105: {2,3,4}
   132: {1,1,2,5}
   147: {2,4,4}
   175: {3,3,4}
   198: {1,2,2,5}
   208: {1,1,1,1,6}
   220: {1,1,3,5}
   245: {3,4,4}
   297: {2,2,2,5}
   308: {1,1,4,5}

Mathematica

Select[Range[1000], PrimePi[FactorInteger[#][[-1, 1]]]-PrimeOmega[#]==1&]

Crossrefs

Positions of 1's in A257541.

Cf. A001222, A047993, A056239, A061395, A063995, A101198, A106529, A112798, A257990, A263297, A325225, A325234, A325235.

Sequence in context: A247420 A063231 A224852 * A030005 A192163 A129307

Adjacent sequences: A325230 A325231 A325232 * A325234 A325235 A325236

Keyword

nonn

Author

Gus Wiseman, Apr 13 2019

Status

approved