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 A147619 Numbers n = concat(a,b) such that phi(n) = phi(a) * phi(b), where phi = A000010. 7
 78, 780, 897, 918, 1179, 1365, 1776, 2574, 2598, 2967, 3168, 3762, 4758, 5775, 5796, 7800, 7875, 7917, 8217, 8970, 9180, 9576, 11790, 13650, 13662, 13875, 13896, 14391, 17760, 18564, 18858, 19812, 20097, 25740, 25935, 25974, 25980, 27573, 28776 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Concat(a,b) means decimal concatenation of a and b, i.e., a*10^[log[10](b)+1] + b, since we do not allow leading zeros in b. However, allowing for leading zeros in b would not give any additional term below 10^6. This sequence was suggested by Farideh Firoozbakht and David Wilson on the SeqFan mailing list, Oct 27 and Nov 06, 2008. Farideh Firoozbakht has proved that if n is in this sequence, then n*10 is again in the sequence. Thus one could call "primitive" elements of this sequence those which aren't a multiple of 10. A possible variant would be to allow decomposition of n into an arbitrary number of substrings. If one requires decomposition of n into each of its digits, i.e. the analog of A098771 with sigma replaced by phi, then 78 appears to be the only number having this property. LINKS Paolo P. Lava, Table of n, a(n) for n = 1..500 MAPLE with(numtheory): P:=proc(q) local s, t, k, n; for n from 1 to q do for k from 1 to ilog10(n) do s:=n mod 10^k; t:=trunc(n/10^k); if s*t>0 then if phi(s)*phi(t)=phi(n) then print(n); break; fi; fi; od; od; end: P(10^5); # Paolo P. Lava, Jan 27 2015 PROG (PARI) is_A147619(n)={ local(p=1, s=eulerphi(n)); while( n>p*=10, n%p*10

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Last modified April 25 04:14 EDT 2019. Contains 322451 sequences. (Running on oeis4.)