A062854 -id:A062854 - cp's OEIS frontend

A108408 Unique values found in A108407. Complement of A108409.

1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 90

Offset: 1

Ralf Stephan, Jun 03 2005

nonn

Cf. A108407, A108409.

terms = 71;
nmax = 3 terms;
A062854 = Table[u = If[n == 1, {}, Union[u, n Range[n]]]; Length[u], {n, 1, nmax + 1}] // Differences // Prepend[#, 1]&;
a108407[n_] := n + 1 - A062854[[n+1]];
Array[a108407, nmax] // Union // Rest // Take[#, terms]& (* Jean-François Alcover, Oct 02 2020 *)

A225253 Number of distinct values of the sum of 2 products of two 0..n integers.

Original entry on oeis.org

1, 3, 8, 16, 27, 42, 59, 81, 105, 134, 167, 203, 241, 285, 331, 381, 436, 495, 556, 622, 690, 764, 841, 920, 1002, 1091, 1184, 1279, 1378, 1482, 1588, 1700, 1813, 1932, 2053, 2177, 2308, 2443, 2579, 2719, 2862, 3012, 3164, 3322, 3481, 3645, 3814, 3985, 4158, 4339

Offset: 0

R. H. Hardin, May 04 2013

nonn

			a(3) = 16 as the possible products i*j where 0 <= i, j <= 3 are 0, 1, 2, 3, 4, 6, 9. From these numbers we can find the 16 distinct sums, listed with a few examples, 0, 1, 2, 3, 4, 5, 6, 7 = 3+4, 8, 9, 10, 11, 12 = 6+6, 13 = 4+9, 15, 18. - _David A. Corneth_, Sep 07 2023

David A. Corneth, Table of n, a(n) for n = 0..3000 (first 999 terms from R. H. Hardin)
David A. Corneth, PARI program

Row 2 of A225252.

Cf. A027384, A062854, A225254.

a(n) = #setbinop((x,y)->x+y, setbinop((x,y)->x*y, [0..n])); \\ Michel Marcus, Sep 06 2023

\\ See PARI link. David A. Corneth, Sep 07 2023

from itertools import combinations_with_replacement
def A225253(n): return len({x+y for x,y in combinations_with_replacement({i*j for i in range(n+1) for j in range(i+1)},2)}) # Chai Wah Wu, Oct 13 2023

a(0)=1 prepended by Alois P. Heinz, Oct 13 2023

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A108408 Unique values found in A108407. Complement of A108409.

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A225253 Number of distinct values of the sum of 2 products of two 0..n integers.

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