cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A350804 Numbers k with exactly one partition into two parts (s,t), s<=t, such that t | s*k.

Original entry on oeis.org

2, 4, 8, 10, 14, 15, 16, 22, 26, 32, 34, 35, 38, 44, 46, 50, 52, 58, 62, 63, 64, 68, 74, 75, 76, 77, 82, 86, 91, 92, 94, 98, 99, 106, 116, 117, 118, 122, 124, 128, 134, 136, 142, 143, 146, 148, 152, 153, 158, 164, 166, 172, 175, 178, 184, 187, 188, 189, 194, 202, 206, 209
Offset: 1

Views

Author

Wesley Ivan Hurt, Jan 16 2022

Keywords

Comments

Numbers k such that k^2 has exactly one divisor d with k/2 <= d < k. - Robert Israel, Jan 08 2025

Examples

			15 is in the sequence since 15 = 6+9 has exactly one partition into two parts (6,9) such that 9 | 6*15 = 90.

Links

Crossrefs

Cf. A338021, A350803 (at least one).

Programs

  • Maple
    filter:= proc(n) nops(select(t -> t >= n/2 and t < n, numtheory:-divisors(n^2)))=1 end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 08 2025
  • PARI
    f(n) = sum(s=1, n\2, !((s*n)%(n-s))); \\ A338021
isok(k) = f(k) == 1; \\ Michel Marcus, Jan 17 2022

A346641 Numbers k with at least one partition into two parts (s,t), s<=t such that t | s*k but no proper divisor of k has this property.

Original entry on oeis.org

2, 15, 35, 63, 77, 91, 99, 117, 143, 153, 187, 209, 221, 247, 299, 323, 325, 357, 391, 399, 425, 437, 475, 483, 493, 513, 527, 551, 575, 589, 609, 621, 651, 667, 703, 713, 725, 759, 775, 777, 783, 837, 851, 861, 899, 925, 943, 957, 989, 999, 1023, 1025, 1073, 1075
Offset: 1

Views

Author

David A. Corneth, Jan 22 2022

Keywords

Comments

Primitive subsequence of A350803.
Odd terms form primitive subsequence of A090196. - Bernard Schott, Jan 23 2022

Examples

			k = 15 = 6 + 9 = s + t is in the sequence (t = 9 | 6*15 = 90 = s*k) but no proper divisor of 15 has this property.

Links

Crossrefs

Cf. A350803.
Subsequence: A082663.

Programs

  • PARI
    upto(n) = { my(v = vector(n, i, -1)); for(i = 1, n, if(v[i] == -1, if(isA350803(i), v[i] = 1; for(j = 2, n\i, v[i*j] = 0; ) ) ) ); select(x->x==1, v, 1) }
isA350803(n) = { for(i = 1, n\2, if((n*i)%(n-i) == 0, return(1) ) ); return(0) }

A350835 Area of the unique integer-sided rectangle with width W, length L, and semiperimeter S_n = L + W, such that L | W*S_n, where S_n = A350804(n).

Original entry on oeis.org

1, 4, 16, 25, 49, 54, 64, 121, 169, 256, 289, 250, 361, 484, 529, 625, 676, 841, 961, 686, 1024, 1156, 1369, 1350, 1444, 1372, 1681, 1849, 2058, 2116, 2209, 2401, 1458, 2809, 3364, 2916, 3481, 3721, 3844, 4096, 4489, 4624, 5041, 2662, 5329, 5476, 5776, 5832, 6241, 6724
Offset: 1

Views

Author

Wesley Ivan Hurt, Jan 17 2022

Keywords

Examples

			a(6) = 54; 54 is the area of the unique 6 X 9 rectangle with semiperimeter A350804(6) = 15 = 6+9, such that 9 | 6*15 = 90.

Links

Crossrefs

Cf. A338021, A350803, A350804.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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