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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

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Last modified September 26 18:11 EDT 2022. Contains 357002 sequences. (Running on oeis4.)