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.

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

A340149 Odd part of A340147: a(n) = A000265(A247074(A003961(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, 3, 23, 15, 27, 1, 15, 5, 21, 9, 13, 33
Offset: 1

Views

Author

Antti Karttunen, Dec 30 2020

Keywords

Comments

Each term a(n) is a divisor of A340075(n), at n=85 occurs the first proper divisor.

Links

Crossrefs

Cf. A000265, A003961, A247074, A340147, A340150 (positions of ones).
Differs from related A340075 for the first time at n=85, where a(85) = 3, while A340075(85) = 9.

Programs

  • PARI
    A000265(n) = (n>>valuation(n,2));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A247074(n) = { my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); }; \\ From A247074
A340149(n) = A000265(A247074(A003961(n)));

Formula

a(n) = A000265(A340147(n)) = A000265(A247074(A003961(n))).

A340076 Positions of ones in A340075.

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 29 2020

Keywords

Comments

Subsequence of A340150 from which this differs for the first time at n=98, as this lacks the term 445 which is present in A340076.
If one applies prime shift (A003961) to each term, and then sorts the results into the ascending order, one gets A340077.

Links

Crossrefs

Cf. A340075, A340077.
Subsequence of A340150.

Programs

Showing 1-3 of 3 results.

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

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