A325503 -id:A325503 - cp's OEIS frontend

A325502 Heinz number of row n of Pascal's triangle A007318.

2, 4, 12, 100, 2548, 407044, 106023164, 136765353124, 399090759725236, 4445098474836287524, 151287513513627682258436, 12698799587219706700017036196, 3463928752077516667634331415766516, 2591202267595530693505786197581910681796

Offset: 0

Gus Wiseman, May 06 2019

The Heinz number of a positive integer sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Every odd-indexed term is a square of a squarefree number.

			Row n = 5 of Pascal's triangle is (1,5,10,10,5,1), with Heinz number prime(1)*prime(5)*prime(10)*prime(10)*prime(5)*prime(1) = 407044, so a(5) = 407044.
The sequence of terms together with their prime indices begins:
                    2: {1}
                    4: {1,1}
                   12: {1,1,2}
                  100: {1,1,3,3}
                 2548: {1,1,4,4,6}
               407044: {1,1,5,5,10,10}
            106023164: {1,1,6,6,15,15,20}
         136765353124: {1,1,7,7,21,21,35,35}
      399090759725236: {1,1,8,8,28,28,56,56,70}
  4445098474836287524: {1,1,9,9,36,36,84,84,126,126}

Index entries for sequences related to Heinz numbers

Cf. A000040, A001222, A001405, A007318, A056239, A112798, A145519, A215366, A325500, A325503, A325505, A325514.

Times@@@Table[Prime[Binomial[n,k]],{n,0,5},{k,0,n}]

A061395(a(n)) = A001405(n).
A056239(a(n)) = A000079(n).
A181819(a(n)) = A038754(n + 1).

A325514 Heinz number of row n of the triangle of partition numbers A008284.

Original entry on oeis.org

2, 2, 4, 8, 24, 72, 600, 4200, 101640, 2042040, 107869080, 6435365640, 644779672680, 62219208188280, 14408598135902520, 3195700205016233640, 1246437353286578234760, 527744165981695537415640, 417665868515500206974318760, 314096677106179199154141208440

Offset: 0

Gus Wiseman, May 07 2019

nonn

The Heinz number of a positive integer sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

			The sequence of terms together with their prime indices begins:
             2: {1}
             2: {1}
             4: {1,1}
             8: {1,1,1}
            24: {1,1,1,2}
            72: {1,1,1,2,2}
           600: {1,1,1,2,3,3}
          4200: {1,1,1,2,3,3,4}
        101640: {1,1,1,2,3,4,5,5}
       2042040: {1,1,1,2,3,4,5,6,7}
     107869080: {1,1,1,2,3,5,5,7,8,9}
    6435365640: {1,1,1,2,3,5,5,7,10,10,11}
  644779672680: {1,1,1,2,3,5,6,7,11,12,13,15}

Index entries for sequences related to Heinz numbers

Cf. A000041, A002569, A008284, A056239, A112798, A145519, A215366, A325500, A325502, A325503, A325512, A325514.

Times@@@Table[If[n>0&&k==0,1,Prime[Length[IntegerPartitions[n,{k}]]]],{n,0,20},{k,0,n}]

A001221(a(n)) = A325512(n).
A061395(a(n)) = A002569(n).
A056239(a(n)) = A000041(n).

cp's OEIS Frontend

A325502 Heinz number of row n of Pascal's triangle A007318.

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