A346277 Primitive terms of A108569.
4, 110, 506, 550, 1830, 2162, 2750, 3422, 4114, 4746, 5490, 5566, 6806, 7782, 9150, 11342, 13750, 14238, 16470, 16762, 23346, 27450, 27722, 31862, 33222, 42714, 43378, 45254, 45750, 49410, 49726, 51302, 61226, 68750, 68906, 70038, 82350, 99238, 99666, 112110, 115650
Offset: 1
Keywords
Examples
a(1) = 4 because every k = 2^m, m >= 2 satisfies phi(k) = phi(k+phi(k)) = 2^(m-1), and k_0 = 4 is the smallest term of this subsequence of A108569. a(2) = 110 because every k = 5*11*2^m, m >= 1 satisfies phi(k) = phi(k+phi(k)) = 5*2^(m+2) and k_0 = 110 is the smallest term of this subsequence of A108569 (note that 5 is a Sophie Germain prime). a(5) = 1830 because every k = 3*5*61*2^m, m >= 1 satisfies phi(k) = phi(k+phi(k)) = 3*5*2^(m+4) and k_0 = 1830 is the smallest term of this subsequence of A108957.
Crossrefs
Programs
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Maple
with(numtheory): for m from 2 to 116000 by 2 do u:=phi(m+phi(m)) - phi(m); if u=0 and phi(m/2 + phi(m/2)) <> phi(m/2) then print(m); else fi; od:
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PARI
f(m) = eulerphi(m+eulerphi(m)) - eulerphi(m); isok(m) = !f(m) && !(m % 2) && f(m/2); \\ Michel Marcus, Aug 31 2021
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