A324587 Heinz numbers of integer partitions of n into distinct perfect squares (A033461).

1, 2, 7, 14, 23, 46, 53, 97, 106, 151, 161, 194, 227, 302, 311, 322, 371, 419, 454, 541, 622, 661, 679, 742, 827, 838, 1009, 1057, 1082, 1193, 1219, 1322, 1358, 1427, 1589, 1619, 1654, 1879, 2018, 2114, 2143, 2177, 2231, 2386, 2437, 2438, 2741, 2854, 2933

Offset

1,2

Comments

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

Also products of distinct elements of A011757.

Links

Table of n, a(n) for n=1..49.

Example

The sequence of terms together with their prime indices begins:
    1: {}
    2: {1}
    7: {4}
   14: {1,4}
   23: {9}
   46: {1,9}
   53: {16}
   97: {25}
  106: {1,16}
  151: {36}
  161: {4,9}
  194: {1,25}
  227: {49}
  302: {1,36}
  311: {64}
  322: {1,4,9}
  371: {4,16}
  419: {81}
  454: {1,49}
  541: {100}

Mathematica

Select[Range[1000], And@@Cases[FactorInteger[#], {p_, k_}:>k==1&&IntegerQ[Sqrt[PrimePi[p]]]]&]

Crossrefs

Cf. A001156, A005117, A011757, A033461, A052335, A056239, A062457, A078135, A112798, A117144, A276078.

Cf. A109298, A324524, A324525, A324571, A324572, A324588.

Sequence in context: A008865 A227582 A249852 * A018392 A051640 A119354

Adjacent sequences: A324584 A324585 A324586 * A324588 A324589 A324590

Keyword

nonn

Author

Gus Wiseman, Mar 08 2019

Status

approved