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A063668
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Numbers of the form 12*k + 2 with nonempty inverse totient set.
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3
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2, 110, 506, 2162, 3422, 4970, 6806, 11342, 13310, 17030, 27722, 31862, 36290, 51302, 56882, 62750, 68906, 96410, 120062, 128522, 146306, 175142, 185330, 195806, 217622, 228962, 240590, 252506, 267674, 316406, 343982, 358202, 417962, 433622, 465806, 516242
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OFFSET
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1,1
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COMMENTS
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Except for the first term, each of these sets contains 2 terms. Other numbers of the form 12*k + 2 have empty inverse totient sets.
Except for the first term, these are numbers of the form (p - 1)*p^(2*e-1) = phi(p^(2*e)) where p is a prime congruent to 11 modulo 12. The inverse totient set for a(n) (n >1) is {p^(2*e), 2*p^(2*e)}.
Numbers k such that A063667((k-2)/12) != 0.
The number of terms <= N is roughly (1/8)*sqrt(N)/log(N). (End)
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LINKS
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EXAMPLE
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1407782 = 1186*1187 where 1187 is a prime congruent to 11 modulo 12, so 1407782 is a term, with invphi(1407782) = {1408969, 2817938} = {1187^2, 2*1187^2}.
267674 = 22*23^3 where 23 is a prime congruent to 11 modulo 12, so 267674 is a term, with invphi(267674) = {279841, 559682} = {23^4, 2*23^4}. - Jianing Song, Dec 30 2018
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PROG
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(PARI) A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1)
isok(n) = my(p=A006530(n), e=if(n>1, valuation(n, p), 1)); (n==2) || (p%12==11&&e%2&&n==(p-1)*p^e) \\ Jianing Song, Dec 30 2018
(PARI) isok(n) = #invphi(n) && !((n-2) % 12); \\ Michel Marcus, Dec 30 2018; using the invphi script by Max Alekseyev
(PARI) isok(m) = !((m-2) % 12) && istotient(m); \\ Michel Marcus, Apr 20 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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