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A338266
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Least prime p such that p*n is not a totient number.
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2
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3, 7, 3, 17, 3, 19, 2, 19, 3, 5, 3, 43, 2, 7, 3, 19, 2, 5, 2, 17, 3, 7, 3, 167, 2, 7, 3, 11, 3, 3, 2, 19, 3, 2, 3, 67, 2, 2, 3, 17, 3, 17, 2, 7, 2, 5, 2, 211, 2, 7, 3, 7, 3, 11, 3, 13, 2, 3, 2, 139, 2, 2, 3, 31, 3, 19, 2, 5, 3, 5, 2, 109, 2, 5, 3, 2, 2, 3, 2
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OFFSET
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1,1
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COMMENTS
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Zhang Ming-Zhi has shown that for every positive integer n, there is a prime p such that p*n is not a totient (see Reference and link, theorem 1).
Differs from A282160, where multiplier p is not requested to be prime, for n = 6, 66, 80, 126, ... those indices where A282160(n) is not prime (see Example).
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REFERENCES
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Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B36, p. 139.
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LINKS
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Zhang Ming-Zhi, On Nontotients, J. Number Theory, Vol. 43, No. 2 (1993), pp. 168-172.
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FORMULA
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EXAMPLE
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a(6) = 19 because 19 * 6 = 114 is not a totient number and 19 is the least prime with this property. Also 15 * 6 = 90 is not either a totient number, so A282160(6) = 15 that is not a prime number.
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PROG
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(PARI) a(n) = my(p=2); while (istotient(p*n), p = nextprime(p+1)); p; \\ Michel Marcus, Oct 19 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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