A293558 - OEIS

A293558

Triangle T(n,k) read by rows: T(n,k) = A005867(k-1)*A002110(n)/A002110(k).

1, 3, 1, 15, 5, 2, 105, 35, 14, 8, 1155, 385, 154, 88, 48, 15015, 5005, 2002, 1144, 624, 480, 255255, 85085, 34034, 19448, 10608, 8160, 5760, 4849845, 1616615, 646646, 369512, 201552, 155040, 109440, 92160

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OFFSET

1,2

COMMENTS

T(n,k) is the triangle in A174909 with reversed row order. (See that sequence for additional comments).

Row sums = A053144(n) = A002110(n) - T(n+1,n+1).

T(n,k) = number of terms with smallest prime factor prime(k) contained in primorial(n) consecutive numbers, k <= n. For example, T(5,4) = 88, so there are 88 terms with smallest prime factor 7 in any sequence of 2310 consecutive numbers.

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

Triangle starts:

n/k 1 2 3 4 5 6

1 1

2 3 1

3 15 5 2

4 105 35 14 8

5 1155 385 154 88 48

6 15015 5005 2002 1144 624 480

T(5,3) = 154: A005867(2) = 2, A002110(5) = 2310, A002110(3) = 30; 2*2310/30 = 154.

MATHEMATICA

Table[#1 Product[EulerPhi@ Prime@ i, {i, k - 1}]/#2 & @@ Map[Product[ Prime@ i, {i, #}] &, {n, k}], {n, 8}, {k, n}] // Flatten (* Michael De Vlieger, Oct 12 2017 *)

CROSSREFS

Cf. A000040 (prime numbers), A002110, A005867, A053144, A174909 (this triangle with reversed row order).

Sequence in context: A293157 A121335 A126454 * A259841 A228540 A144815

Adjacent sequences: A293555 A293556 A293557 * A293559 A293560 A293561

KEYWORD

nonn,tabl

AUTHOR

Bob Selcoe, Oct 11 2017

STATUS

approved