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.

A340151 Setwise difference A340150 \ A340076.

Original entry on oeis.org

445, 527, 935, 1207, 1577, 1595, 1705, 1711, 2101, 2145, 2201, 2507, 3245, 3315, 4895, 6045, 6631, 6931, 7511, 8371, 9707, 9845, 10189, 10295, 10505, 11023, 11895, 12137, 12194, 13145, 13571, 13845, 14101, 14245, 15042, 15281, 16235, 16643, 17355, 17701, 18559, 19567, 20119, 20865, 22703, 23347, 25123, 26581, 27101, 27695
Offset: 1

Views

Author

Antti Karttunen, Dec 30 2020

Keywords

Comments

Positions k where A340149(k) = 1, but A340075(k) > 1.

Crossrefs

Setwise difference A340150 \ A340076.
Cf. A340091 (gives the same terms prime shifted once and sorted into ascending order).
Cf. A340075, A340149.

Programs

A340075 The odd part of A340072(n).

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 1, 9, 5, 3, 1, 3, 1, 5, 3, 27, 1, 5, 1, 9, 5, 3, 1, 9, 7, 1, 25, 15, 1, 3, 1, 81, 3, 9, 15, 15, 1, 11, 1, 27, 1, 5, 1, 9, 5, 7, 1, 27, 11, 21, 9, 3, 1, 25, 1, 45, 11, 15, 1, 9, 1, 9, 25, 243, 3, 3, 1, 27, 7, 3, 1, 45, 1, 5, 21, 33, 15, 1, 1, 81, 125, 21, 1, 15, 9, 23, 15, 27, 1, 15, 5, 21, 9, 13, 33, 81
Offset: 1

Views

Author

Antti Karttunen, Dec 28 2020

Keywords

Comments

Each term a(n) is a multiple of A340149(n), therefore, as both sequences have only positive terms, it follows that if a(n) = 1 then A340149(n) = 1 also, but not necessarily vice versa.

Links

Crossrefs

Cf. A000265, A003961, A019565, A339901, A339904, A340072, A340074, A340076 (positions of ones), A340149 (differs from the first time at n=85).

Programs

Formula

a(n) = A000265(A340072(n)).
a(n) = A339904(n) / A340074(n) = A339904(n) / gcd(A003961(n)-1, A339904(n)).
For all n >= 0, a(A019565(n)) = A339901(n).

A340077 Odd numbers k for which k-1 is a multiple of A053575(k) [the odd part of phi(k)].

Original entry on oeis.org

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51, 53, 59, 61, 67, 71, 73, 79, 83, 85, 89, 91, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 255, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313
Offset: 1

Views

Author

Antti Karttunen, Dec 29 2020

Keywords

Comments

Sequence A003961(A340076(i)), i = 1.., sorted into ascending order. In other words, this sequence consists of such odd numbers k that A064989(k) is in A340076.

Links

Crossrefs

Cf. A064989, A340075, A340076.
Subsequence of A339879.
Subsequences: A065091, A339880 (composite terms), A339869, A339870 (and their further subsequences).

Programs

  • PARI
    A000265(n) = (n>>valuation(n, 2));
isA340077(n) = ((n%2)&&!((n-1)%A000265(eulerphi(n))));
  • PARI
    A064989(n) = { my(f=factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f) };
isA340077(n) = ((n%2)&&(1==A340075(A064989(n)))); \\ Needs also code from A340075.

A340150 Positions of ones in A340149.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 23, 26, 29, 31, 37, 39, 41, 43, 47, 53, 55, 59, 61, 67, 71, 73, 78, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 138, 139, 149, 151, 157, 163, 167, 173, 179, 181, 182, 191, 193, 195, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 259, 263, 269, 271, 277, 281, 283
Offset: 1

Views

Author

Antti Karttunen, Dec 30 2020

Keywords

Comments

Differs from its subsequence A340076 for the first time at n=98, where occurs the first term 445, which is not present in A340076. See A340151.

Links

Crossrefs

Cf. A340076, A340149, A340151 (for terms not present in A340076).

Programs

Showing 1-4 of 4 results.

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