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 1-4 of 4 results.

A339907 Odd squarefree numbers k > 1 for which the bigomega(phi(k)) <= bigomega(k-1), where bigomega gives the number of prime divisors, counted with multiplicity.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 21, 23, 29, 31, 33, 37, 41, 43, 47, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 129, 131, 137, 139, 141, 145, 149, 151, 157, 161, 163, 167, 173, 177, 179, 181, 191, 193, 197, 199, 201, 209, 211, 217, 223, 227, 229, 233, 235, 239, 241, 249, 251, 253, 257
Offset: 1

Views

Author

Antti Karttunen, Dec 21 2020

Keywords

Comments

Terms of A003961(A019565(A339906(i))) [or equally, of A019565(2*A339906(i))], for i = 1.., sorted into ascending order.
Natural numbers n > 2 that satisfy equation k * phi(n) = n - 1 (for some integer k) all occur in this sequence. Lehmer conjectured that there are no composite solutions.

Links

Crossrefs

Cf. A339906.
Cf. A065091, A339908 (subsequences).
Cf. also A339817.
Apart from initial 3, a subsequence of A339910.

Programs

  • PARI
    isA339907(n) = ((n>1)&&(n%2)&&issquarefree(n)&&(bigomega(eulerphi(n))<=bigomega(n-1)));

A339911 Numbers k > 1 for which bigomega(k) <= bigomega(k-1)/2, where bigomega gives the number of prime factors, counted with multiplicity.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 33, 37, 41, 43, 47, 49, 53, 55, 57, 59, 61, 65, 67, 71, 73, 79, 82, 83, 85, 89, 91, 97, 101, 103, 107, 109, 113, 121, 127, 129, 131, 133, 137, 139, 141, 145, 149, 151, 157, 161, 163, 167, 169, 173, 177, 179, 181, 185, 191, 193, 197, 199, 201, 205, 209, 211, 217, 221, 223, 226, 227
Offset: 1

Views

Author

Antti Karttunen, Dec 22 2020

Keywords

Links

Crossrefs

Cf. A001222.
Subsequence of A339910.
Cf. A339908, A339912 for subsequences.

Programs

  • Mathematica
    Select[Range[3, 227, 2], PrimeOmega[#] <= PrimeOmega[# - 1]/2 &] (* Michael De Vlieger, Dec 22 2020 *)
  • PARI
    isA339911(n) = ((n>1)&&((2*bigomega(n))<=bigomega(n-1)));

A339912 Numbers k > 1 for which bigomega(k) < bigomega(k-1)/2, where bigomega gives the number of prime factors, counted with multiplicity.

Original entry on oeis.org

13, 17, 19, 29, 31, 33, 37, 41, 43, 49, 53, 61, 65, 67, 71, 73, 79, 89, 97, 101, 103, 109, 113, 121, 127, 129, 131, 137, 139, 145, 149, 151, 157, 161, 163, 169, 173, 177, 181, 191, 193, 197, 199, 201, 209, 211, 217, 223, 229, 233, 239, 241, 251, 253, 257, 265, 269, 271, 277, 281, 283, 289, 293, 301, 305, 307, 311, 313
Offset: 1

Views

Author

Antti Karttunen, Dec 22 2020

Keywords

Links

Crossrefs

Cf. A001222.
Subsequence of A339911 and of A339910.
Cf. also A339908.

Programs

A363049 Even numbers k having fewer prime factors, counted with multiplicity, than k-1.

Original entry on oeis.org

46, 82, 106, 118, 166, 190, 226, 244, 262, 274, 298, 316, 326, 334, 346, 358, 386, 406, 442, 466, 478, 514, 526, 562, 568, 586, 622, 626, 676, 694, 706, 730, 766, 778, 802, 826, 838, 862, 886, 892, 898, 926, 946, 958, 982, 1006, 1018, 1030, 1046, 1054, 1090
Offset: 1

Views

Author

Alexandre Herrera, May 14 2023

Keywords

Examples

			46 = 2*23, so A001222(46) = 2, and 45 = 3*3*5, so A001222(45) = 3, thus 46 is a term of the sequence.

Crossrefs

Cf. A001222 (bigomega), A339910 (both odd and even).

Programs

  • Mathematica
    Select[2Range[550],PrimeOmega[#]Stefano Spezia, May 15 2023 *)
  • PARI
    isok(n) = n%2==0 && bigomega(n) < bigomega(n-1) \\ Andrew Howroyd, May 14 2023
Showing 1-4 of 4 results.

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

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