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.

A354362 Intersection of A228058 and A260021.

Original entry on oeis.org

45, 49005, 597861, 715473, 1538757, 1891593, 1893213, 2714877, 3067713, 3890997, 4126221, 4479057, 5302341, 5465313, 5793525, 5890437, 6008013, 6478461, 6596073, 6882525, 7184133, 7419357, 8595477, 9771597, 10712493, 11300553, 11771001, 11888613, 12123837, 12947121, 13535181, 14240853, 15887421, 16240257, 17181153
Offset: 1

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Author

Antti Karttunen, May 24 2022

Keywords

Links

Crossrefs

Cf. A228058, A260021.
Subsequence of A353679.
Cf. also A354106.

Programs

A006872 Numbers k such that phi(k) = phi(sigma(k)).

Original entry on oeis.org

1, 3, 15, 26, 39, 45, 74, 104, 111, 117, 122, 146, 175, 183, 195, 219, 296, 314, 333, 357, 386, 471, 488, 549, 554, 555, 579, 584, 585, 608, 626, 646, 657, 794, 831, 842, 914, 915, 939, 962, 1071, 1082, 1095, 1191, 1226, 1256, 1263, 1292, 1322, 1346
Offset: 1

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Author

Jeffrey Shallit, N. J. A. Sloane

Keywords

References

  • S. W. Golomb, Equality among number-theoretic functions, Abstract 882-11-16, Abstracts Amer. Math. Soc., 14 (1993), 415-416.
  • R. K. Guy, Unsolved Problems in Number Theory, B42.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A000010, A000203, A062401, A353637 (characteristic function).
Positions of zeros in A353636.
Setwise difference of A353684 and A353683, and also of A353685 and A353686.
Intersection of A353684 and A353685.
Subsequences: A260021, A353634, A353635, A353679 (odd terms).
Cf. also A033631, A033632, A067880, A137815, A260020.

Programs

  • Haskell
    a006872 n = a006872_list !! (n-1)
a006872_list = filter (\x -> a000010' x == a000010' (a000203' x)) [1..]
-- Reinhard Zumkeller, Jul 14 2015
  • Magma
    [n:n in [1..2000]| EulerPhi(SumOfDivisors(n)) eq EulerPhi(n)]; // Marius A. Burtea, Jan 01 2019
  • Mathematica
    Select[Range@ 1350, EulerPhi@ # == EulerPhi@ DivisorSigma[1, #] &] (* Michael De Vlieger, Jan 01 2019 *)
  • PARI
    lista(nn) = {for (i=1, nn, if (eulerphi(i)==eulerphi(sigma(i)), print1(i, ", ")););} \\ Michel Marcus, May 25 2013

Extensions

More terms from Jud McCranie

A354345 Numbers k such that k = x * A005383(i), where x is either 2, 3, 8, 9 or 15 and i > 2 [i.e., A005383(i) > 5].

Original entry on oeis.org

26, 39, 74, 104, 111, 117, 122, 146, 183, 195, 219, 296, 314, 333, 386, 471, 488, 549, 554, 555, 579, 584, 626, 657, 794, 831, 842, 914, 915, 939, 1082, 1095, 1191, 1226, 1256, 1263, 1322, 1346, 1371, 1413, 1466, 1514, 1544, 1623, 1737, 1754, 1839, 1983, 1994, 2019, 2186, 2199, 2216, 2271, 2306, 2355, 2402, 2426
Offset: 1

Views

Author

Antti Karttunen, May 25 2022

Keywords

Comments

Solutions to phi(n) = phi(sigma(n)) that are given by Theorem 3 of Golomb's manuscript, i.e., a subset of all solutions (A006872).

Links

Crossrefs

Setwise difference A006872 \ A260021. Subset of positions of zeros in A353636.
Cf. A005383, A354344 (characteristic function).

Programs

  • PARI
    A354344(n) = { if(!(n%15),n/=15,if(!(n%9),n/=9,if(!(n%8),n/=8,if(!(n%3),n/=3,if(!(n%2),n/=2,return(0)))))); ((n>5) && isprime(n) && isprime((1+n)/2)); };
isA354345(n) = A354344(n);

Formula

For all n >= 1, A353636(a(n)) = 0.
Showing 1-3 of 3 results.

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

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