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.

A176552 Complement of A174894, where A174894 = numbers such that both arithmetic means of distinct and all prime factors are integers.

Original entry on oeis.org

1, 6, 10, 12, 14, 18, 20, 22, 24, 26, 28, 30, 34, 36, 38, 40, 44, 45, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 66, 68, 70, 72, 74, 75, 76, 80, 82, 84, 86, 88, 90, 82, 94, 96, 98, 99, 100
Offset: 1

Views

Author

Jaroslav Krizek, Apr 20 2010

Keywords

Comments

For these numbers hold that both arithmetic means of distinct and all prime factors are not integers or only one of these means is an integer.

A175397 Numbers such that both arithmetic means of distinct and all prime factors are not integers.

Original entry on oeis.org

1, 6, 10, 12, 14, 18, 22, 24, 26, 28, 30, 34, 36, 38, 40, 46, 48, 52, 54, 56, 58, 62, 66, 70, 72, 74, 76, 80, 82, 86, 88, 90, 94, 96, 98, 100, 102, 104, 106, 108, 118, 120, 122, 124, 130, 132, 134, 136, 138, 142, 144, 146, 148, 150, 152, 154, 158, 160, 162, 165, 166, 172, 174, 176, 178, 182, 184
Offset: 1

Views

Author

Jaroslav Krizek, May 01 2010

Keywords

Comments

Contains all even semiprimes. - Robert Israel, Nov 10 2024

Examples

			For a(13) = 36: 36 = 2^2*3^3; both (2+2+3+3)/4 and (2+3)/2 are not integers.

Links

Crossrefs

Subsequence of A176552, A175352 and A176587. Complement of A175418. Cf. A174894.

Programs

  • Maple
    filter:= proc(n) local F,t,m;
  F:= ifactors(n)[2]; m:= nops(F);
  not (add(t[1],t=F)/m)::integer and not (add(t[1]*t[2],t=F)/add(t[2],t=F))::integer
end proc:
filter(1):= true:
select(filter, [$1..1000]); # Robert Israel, Nov 10 2024

Extensions

a(27) corrected, and more terms from Robert Israel, Nov 10 2024

A175418 Complement of A175397, where A175397 = numbers such that both arithmetic means of distinct and all prime factors are not integers.

Original entry on oeis.org

2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 20, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 42, 43, 44, 45, 47, 49, 50, 51, 53, 55, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 73, 75, 77, 78, 79, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 99
Offset: 1

Views

Author

Jaroslav Krizek, May 09 2010

Keywords

Comments

For these numbers hold that both arithmetic means of distinct and all prime factors are integers or only one of these means is an integer.
Includes all prime powers and odd semiprimes. - Robert Israel, Nov 10 2024

Links

Crossrefs

Cf. A174894, A176552, A175352, A175397, A176587.

Programs

  • Maple
    filter:= proc(n) local F,t;
  F:= ifactors(n)[2];
  (add(t[1],t=F)/nops(F))::integer or (add(t[1]*t[2],t=F)/add(t[2],t=F))::integer
end proc:
select(filter, [$2..100]); # Robert Israel, Nov 10 2024

Extensions

a(49) corrected by Robert Israel, Nov 10 2024
Showing 1-3 of 3 results.

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

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