A325407 Nonprime Heinz numbers of multiples of triangular partitions, or of finite arithmetic progressions with offset 0.

1, 6, 21, 30, 65, 133, 210, 273, 319, 481, 731, 1007, 1403, 1495, 2059, 2310, 2449, 3293, 4141, 4601, 4921, 5187, 5311, 6943, 8201, 9211, 10921, 12283, 13213, 14993, 15247, 16517, 19847, 22213, 24139, 25853, 28141, 29341, 29539, 30030, 31753, 37211, 40741

Offset

1,2

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers of the form Product_{k = 1...b} prime(k * c) for some b > 1 and c > 0.

Links

Table of n, a(n) for n=1..43.

Example

The sequence of terms together with their prime indices begins:
      1: {}
      6: {1,2}
     21: {2,4}
     30: {1,2,3}
     65: {3,6}
    133: {4,8}
    210: {1,2,3,4}
    273: {2,4,6}
    319: {5,10}
    481: {6,12}
    731: {7,14}
   1007: {8,16}
   1403: {9,18}
   1495: {3,6,9}
   2059: {10,20}
   2310: {1,2,3,4,5}
   2449: {11,22}
   3293: {12,24}
   4141: {13,26}
   4601: {14,28}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[10000], !PrimeQ[#]&&SameQ@@Differences[Prepend[primeMS[#], 0]]&]

Crossrefs

Cf. A007294, A007862, A049988, A056239, A112798, A325327, A325328, A325355, A325359, A325367, A325390.

Sequence in context: A347875 A287165 A280296 * A239920 A173622 A302868

Adjacent sequences: A325404 A325405 A325406 * A325408 A325409 A325410

Keyword

nonn

Author

Gus Wiseman, May 03 2019

Status

approved