The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A350086 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A350086

a(n) is the smallest totient number k > 1 such that A005277(n)*k is a nontotient number, or 0 if no such number exists.
(history; published version)

#15 by Michael De Vlieger at Sat Mar 11 10:11:30 EST 2023

STATUS

proposed

approved

#14 by Michel Marcus at Sat Mar 11 10:09:11 EST 2023

STATUS

editing

proposed

#13 by Michel Marcus at Sat Mar 11 10:08:25 EST 2023

LINKS

Michel Marcus, <a href="/A350086/b350086.txt">Table of n, a(n) for n = 1..8458</a>

STATUS

approved

editing

Discussion

Sat Mar 11

10:09

Michel Marcus: bfile for list(30000)

#12 by N. J. A. Sloane at Fri Dec 17 20:58:51 EST 2021

STATUS

proposed

approved

#11 by Jianing Song at Fri Dec 17 11:45:35 EST 2021

STATUS

editing

proposed

#10 by Jianing Song at Fri Dec 17 11:41:28 EST 2021

COMMENTS

Conjecture: Conjecture: every totient number > 1 which is not of the form m*m', where m > 1 is a totient and m' > 1 is in A301587, appears in this sequence. For example, the numbers 2, 6, 10, 18, 22, 28, 30 first appears when A007617(n) = 7, 15, 5, 33, 11, 902, 3.

EXAMPLE

A005277(7399111) = 241010 90. N = 106 is a nontotient totient number > 1 such that 24101090*k is a totient for totient numbers 2 <= k < 100, N, and that 24101090*100 N is a nontotient, so a(7399111) = 100. Note that although 100 = 10*10 is a product of 2 totient number > 1, neither factor is in A301587, so nothing prevents that 100 is a term of this sequence106.

A005277(83) = 450. N = 2010 is a totient number > 1 such that 450*k is a totient for totient numbers 2 <= k < N, and 450*N is a nontotient, so a(83) = 2010.

A005277(187) = 902. N = 28 is a totient number > 1 such that 902*k is a totient for totient numbers 2 <= k < N, and 902*N is a nontotient, so a(187) = 28.

A005277(73991) = 241010. N = 100 is a totient number > 1 such that 241010*k is a totient for totient numbers 2 <= k < N, and 241010*N is a nontotient, so a(73991) = 100. Note that although 100 = 10*10 is a product of 2 totient number > 1, neither factor is in A301587, so nothing prevents that 100 is a term of this sequence.

#9 by Jianing Song at Fri Dec 17 11:33:36 EST 2021

EXAMPLE

A005277(73991) = 241010 is a nontotient number such that 241010*k is a totient for totient numbers 2 <= k < 100, and that 241010*100 is a nontotient, so a(73991) = 100. Note that although 100 = 10*10 is a product of 2 totient number > 1, neither factor is in A301587, so nothing prevents that 100 is a term of this sequence.

#8 by Jianing Song at Fri Dec 17 11:27:45 EST 2021

COMMENTS

Conjecture: (i) no term is the product of at least 2 totient numbers > 1 (the smallest such number not excluded by the previous comment is 10*10 = 100); (ii) Conjecture: every totient number > 1 which is not a product of at least 2 the form m*m', where m > 1 is a totient numbers and m' > 1 is in A301587, appears in this sequence. For example, the numbers 2, 6, 10, 18, 22, 28, 30 first appears when A007617(n) = 7, 15, 5, 33, 11, 902, 3.

STATUS

proposed

editing

#7 by Jianing Song at Fri Dec 17 11:21:31 EST 2021

STATUS

editing

proposed

#6 by Jianing Song at Fri Dec 17 11:21:26 EST 2021

CROSSREFS

Cf. A005277, A350085, A301587.