login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181662 a(n) is the smallest positive integral multiple of 2^n not in the range of the Euler phi function. 2
3, 14, 68, 152, 304, 608, 1984, 3968, 12032, 24064, 48128, 96256, 192512, 385024, 770048, 1540096, 3080192, 6160384, 12320768, 24641536, 49283072, 98566144, 197132288, 394264576, 788529152, 1577058304, 3154116608, 6308233216, 12616466432, 25232932864, 50465865728, 100931731456 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From Jianing Song, Dec 14 2021: (Start)

Let a(n) = 2^n * k, then k must be odd, otherwise a(n)/2 is a totient number, which implies that a(n) is a totient.

Note that 271129 * 2^m is a nontotient for all m (see A058887), so k <= 271129. In fact, let p be smallest prime such that 2^e*p + 1 is composite for all 0 <= e <= n, then k <= p (since 2^n*p is a nontotient).

Actually, k is equal to p. To verify this, it suffices to show that k cannot be an odd composite number < 271129; that is to say, if 2^n * k is a nontotient for an odd composite number < 271129, then there exists k' < k such that 2^n * k' is a nontotient.

The case k < 383 can be easily checked. Let k be an odd composite number in the range (383, 271129), k * 2^n is a nontotient implies n < 2554 unless k = 98431 or 248959 (see the a-file below), then 383 * 2^n is a nontotient (the least n such that 383 * 2^n + 1 is prime is n = 6393). For k = 98431 or 248959, k * 2^n is a nontotient implies n < 7062, then 2897 * 2^n is a nontotient (the least n such that 2897 * 2^n + 1 is prime is n = 9715. (End)

REFERENCES

David Harden, Posting to Sequence Fans Mailing List, Sep 19 2010.

LINKS

Table of n, a(n) for n=0..31.

Jianing Song, List of odd composites < 271129 such that the smallest n such that k * 2^n is a totient is greater than 100.

FORMULA

a(n) = A058887(n)*2^n.

CROSSREFS

Cf. A005277, A007617, A058887, A040076, A057192.

Sequence in context: A002320 A151323 A354503 * A241478 A113140 A151324

Adjacent sequences: A181659 A181660 A181661 * A181663 A181664 A181665

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 18 2010

EXTENSIONS

Escape clause removed by Jianing Song, Dec 14 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 13:02 EST 2022. Contains 358656 sequences. (Running on oeis4.)