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.

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A338561 a(n) is the least m such that A338266(m) = prime(n), where A338266(m) is the least prime p such that p*m is not a totient number.

Original entry on oeis.org

7, 1, 10, 2, 28, 56, 4, 6, 460, 232, 64, 300, 328, 12, 256, 180, 176, 84, 36, 132, 1400, 984, 2200, 780, 1332, 280, 1664, 1672, 72, 8136, 420, 53244, 1960, 60, 2320, 5928, 264, 936, 24, 32604, 6696, 2976, 2268, 6372, 312, 1380, 48, 320, 2560, 816, 16500, 4860
Offset: 1

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Author

Bernard Schott, Nov 02 2020

Keywords

Comments

Zhang Ming-Zhi has shown that for every positive integer m, there is a prime p such that m*p is not a totient (see Reference, link: theorem 1). A338266 gives the smallest prime p that is such linked to m.

Examples

			Prime(2)=3 is the smallest prime such that 3*1=3, 3*3=9, 3*9=27, 3*11=33, 3*15=45,... are not totient (A338266), and 1 is the smallest number of the set {1, 3, 9, 11, 15...} linked to prime(2), so a(2)=1.

References

  • Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B36, p. 139.

Links

  • Zhang Ming-Zhi, On Nontotients, J. Number Theory, Vol. 43, No. 2 (1993), pp. 168-172.

Crossrefs

Cf. A000010, A002202, A007617, A071615, A338266.

Programs

  • PARI
    f(n) = my(p=2); while (istotient(p*n), p = nextprime(p+1)); p; \\ A338266
a(n) = my(k=1, p=prime(n)); while(f(k) != p, k++); k; \\ Michel Marcus, Nov 03 2020

Extensions

More terms from Amiram Eldar, Nov 02 2020
Name improved by Amiram Eldar and Michel Marcus, Nov 03 2020
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