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.

A217140 a(n) = m/n where m is the least number divisible by n such that phi(m) = phi(m+6n).

Original entry on oeis.org

24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 60, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36, 24, 24, 24, 24, 36
Offset: 1

Views

Author

Michel Marcus and Jonathan Sondow, Oct 01 2012

Keywords

Examples

			A179188(1)=24 is divisible by 1 and the quotient is 24, so a(1)=24.
A217139(1)=48 is divisible by 2 and the quotient is 24, so a(2)=24.
The first solution to phi(n)=phi(n+18) to be divisible by 3 is 72 and the quotient is 24, so a(3)=24.

Links

Crossrefs

Cf. A007015, A179188, A217139, A217141, A217068.

A217142 Least number m such that phi(m) = phi(m+6n) and m is not divisible by n.

Original entry on oeis.org

143, 52, 101, 124, 104, 123, 183, 156, 248, 144, 208, 267, 241, 365, 219, 248, 312, 306, 496, 369, 288, 432, 241, 543, 369, 468, 482, 386, 730, 444, 438, 432, 496, 1220, 624, 779, 612, 801, 915, 744, 723, 582, 576, 1095, 864, 488, 482, 641, 1086, 674, 738
Offset: 2

Views

Author

Michel Marcus, Sep 27 2012

Keywords

Links

Crossrefs

Cf. A000010, A179188, A217068, A217139, A217141.

Programs

  • PARI
    fpr(Nmax, lim) = {for (i=2, Nmax,N = i*6;op = vector(N);f = 0;for (n=1, lim, if (op[n%N+1]+0==op[n%N+1]=eulerphi(n), if ((n-N) % i != 0, f = n-N;break;);););print1(f, ", "););}

A217619 a(n) = m/(12*n) where m is the least multiple of n that satisfies phi(m) = phi(m+6*n).

Original entry on oeis.org

2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2
Offset: 1

Views

Author

Jonathan Sondow and Michel Marcus, Oct 09 2012

Keywords

Comments

It appears that A217140(n) is divisible by 12 for all n.

Examples

			A179188(1)=24 is divisible by 1 and the quotient 24 when divided by 12 gives 2, so a(1)=2.
A217139(1)=48 is divisible by 2 and the quotient 24 when divided by 12 gives 2, so a(2)=2.
A217140(5)=36 and 36/12=3, so a(5)=3.

Links

  • S. W. Graham, J. J. Holt and C. Pomerance, On the solutions to phi(n) = phi(n+k), Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 867-882.

Crossrefs

Cf. A179188, A217139, A217141, A217068, A217140.

Formula

a(n) = A217140(n)/12.
Showing 1-3 of 3 results.

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

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