A325994 Heinz numbers of integer partitions such that not every ordered pair of distinct parts has a different quotient.

42, 84, 126, 168, 210, 230, 252, 294, 336, 378, 390, 399, 420, 460, 462, 504, 546, 588, 630, 672, 690, 714, 742, 756, 780, 798, 840, 882, 920, 924, 966, 1008, 1050, 1092, 1134, 1150, 1170, 1176, 1197, 1218, 1260, 1302, 1344, 1365, 1380, 1386, 1428, 1470, 1484

Offset

1,1

Comments

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..49.

Example

The sequence of terms together with their prime indices begins:
    42: {1,2,4}
    84: {1,1,2,4}
   126: {1,2,2,4}
   168: {1,1,1,2,4}
   210: {1,2,3,4}
   230: {1,3,9}
   252: {1,1,2,2,4}
   294: {1,2,4,4}
   336: {1,1,1,1,2,4}
   378: {1,2,2,2,4}
   390: {1,2,3,6}
   399: {2,4,8}
   420: {1,1,2,3,4}
   460: {1,1,3,9}
   462: {1,2,4,5}
   504: {1,1,1,2,2,4}
   546: {1,2,4,6}
   588: {1,1,2,4,4}
   630: {1,2,2,3,4}
   672: {1,1,1,1,1,2,4}

Mathematica

Select[Range[1000], !UnsameQ@@Divide@@@Subsets[PrimePi/@First/@FactorInteger[#], {2}]&]

Crossrefs

The subset case is A325860.

The maximal case is A325861.

The integer partition case is A325853.

The strict integer partition case is A325854.

Heinz numbers of the counterexamples are given by A325994.

Cf. A002033, A056239, A103300, A108917, A112798, A143823, A196724, A325768, A325856, A325868, A325869, A325876.

Sequence in context: A153644 A172437 A160283 * A352481 A019283 A331365

Adjacent sequences: A325991 A325992 A325993 * A325995 A325996 A325997

Keyword

nonn

Author

Gus Wiseman, Jun 02 2019

Status

approved