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A350320
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Totient numbers k such that 10*k is a nontotient.
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5
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110, 13310, 18260, 78980, 130460, 143660, 163460, 164780, 167420, 284900, 325160, 329780, 332420, 370700, 381260, 403700, 418220, 431420, 453860, 514580, 526460, 535700, 554180, 560780, 603020, 628100, 646580, 665060, 675620, 732380, 745580, 765380, 801020
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OFFSET
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1,1
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COMMENTS
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10 is the smallest totient number that is not in A301587.
If 10*phi(m) is a nontotient, then m is divisible by 121 but not by 5, so every term is divisible by 110.
Proof. In the following cases, 10*phi(m) is a totient number:
(a) If m is not divisible by 11, then phi(11*m) = phi(11)*phi(m) = 10*phi(m).
(b) If m is divisible by 11 but not by 121 or 5, then phi((m/11)*125) = phi(m/11)*phi(125) = (phi(m)/10)*100 = 10*phi(m).
(c) If m is divisible by 5 but not by 2, then phi(4*5*m) = phi(4)*phi(5*m) = 2*(5*phi(m)) = 10*phi(m).
(d) If m is divisible by 5 and 2, then phi(10*m) = 10*phi(m).
So the only left case is that m is divisible by 121 but not by 5.
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LINKS
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Table of n, a(n) for n=1..33.
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EXAMPLE
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110 is a term since 110 = phi(121) = phi(242), but phi(n) = 10*110 = 1100 has no solution.
13310 is a term since 13310 = phi(14641) = phi(29282), but phi(n) = 10*13310 = 133100 has no solution.
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PROG
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(PARI) isA350320(n) = istotient(n) && !istotient(10*n)
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CROSSREFS
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Totient numbers k such that m*k is a nontotient: A350316 (m=3), A350317 (m=5), A350318 (m=7), A350319 (m=9), this sequence (m=10), A350321 (m=14).
Cf. A002202, A005277, A301587.
Sequence in context: A285696 A097580 A216786 * A295444 A295436 A246635
Adjacent sequences: A350317 A350318 A350319 * A350321 A350322 A350323
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KEYWORD
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nonn
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AUTHOR
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Jianing Song, Dec 24 2021
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STATUS
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approved
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