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SUMMARY:Mohan (BK Birla Institute of Engineering and Technology\, Pilani\,
  India)
DTSTART:20260717T150000Z
DTEND:20260717T152500Z
DTSTAMP:20260710T111639Z
UID:CANT2026/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/63/
 ">Lehmer-type conjectures and open problems for Nathanson’s totient func
 tions</a>\nby Mohan (BK Birla Institute of Engineering and Technology\, Pi
 lani\, India) as part of Combinatorial and additive number theory seminar 
 (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate Center 
 (4th floor).\n\nAbstract\nNathanson’s totient functions $\\Phi(n)$ and $
 \\Phi_k(n)$\, where $\\Phi(n)$ counts the number of nonempty sets $A \\sub
 seteq \\{1\, 2\, \\dots\, n\\}$ for which $\\gcd(A)$ is relatively prime t
 o $n$\, and $\\Phi_k(n)$ restricts those of size $k$. We formulate and ana
 lyze some analogue of Lehmer's conjecture in the setting of Nathanson’s 
 totient functions $\\Phi(n)$ and $\\Phi_k(n)$. We further discuss divisibi
 lity phenomena for $\\Phi(n)$. We conclude with several conjectures and op
 en problems concerning density\, arithmetic progressions\, and further str
 uctural properties of these functions.\n
LOCATION:https://researchseminars.org/talk/CANT2026/63/
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