A369979 Three-dimensional array giving all products of three (not necessarily distinct) odd primes.

27, 45, 75, 125, 63, 105, 175, 147, 245, 343, 99, 165, 275, 231, 385, 539, 363, 605, 847, 1331, 117, 195, 325, 273, 455, 637, 429, 715, 1001, 1573, 507, 845, 1183, 1859, 2197, 153, 255, 425, 357, 595, 833, 561, 935, 1309, 2057, 663, 1105, 1547, 2431, 2873, 867, 1445, 2023, 3179, 3757, 4913, 171, 285, 475, 399, 665, 931

Offset: 1

Author

Antti Karttunen, Mar 09 2024

Keywords

• nonn
• tabf

Comments

For n > 20, a(n) < A370138(n).

Examples

			Table T(x,y,z) = A065091(x) * A065091(y) * A065091(z), x >= y >= z >= 1, is read by lexicographical ordering of weakly decreasing triplets (x,y,z):
(1, 1, 1) -> 3*3*3 = 27;
(2, 1, 1) -> 5*3*3 = 45, (2, 2, 1) -> 5*5*3 = 75, (2, 2, 2) -> 5*5*5 = 125;
(3, 1, 1) -> 7*3*3 = 63, (3, 2, 1) -> 7*5*3 = 105, (3, 2, 2) -> 7*5*5 = 175, (3, 3, 1) -> 7*7*3 = 147, (3, 3, 2) -> 7*7*5 = 245, (3, 3, 3) -> 7*7*7 = 343.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..15180

Crossrefs

Cf. A000292, A046316 (same sequence sorted into ascending order), A065091, A276086, A370137, A370138.

Cf. also A087112.

Programs

Mathematica

Table[Prime[i]*Prime[j]*Prime[k], {i, 2, 8}, {j, 2, i}, {k, 2, j}] // Flatten (* Michael De Vlieger, Mar 09 2024 *)

PARI

up_to = 15180;
A369979list(up_to) = { my(v = vector(up_to), i=0); for(x=1,oo, for(y=1,x, for(z=1,y, i++; if(i > up_to, return(v)); v[i] = prime(1+x)*prime(1+y)*prime(1+z)))); (v); };
v369979 = A369979list(up_to);
A369979(n) = v369979[n];

Formula

For n > 1, a(n) = A276086(A370137(n)).