A258319 Numbers n such that n = concat(a,b) and n = phi(n) + phi(a) + phi(b), with a>0 and b>0, where phi(n) is the Euler totient function of n.
25, 177, 1177, 2501, 17105, 21337, 22681, 32581, 217009, 409501, 561601, 577501, 861841, 1025821, 1401841, 1738081, 2836465, 8331361, 10284193, 19971901, 20103001, 27835921, 31949921, 34897501, 100763053, 107314217, 111512701, 121806001, 150658561, 155874001
Offset: 1
Examples
25 = concat(2,5); phi(25) + phi(2) + phi(5) = 20 + 1 + 4 = 25; 177 = concat(1,77); phi(177) + phi(1) + phi(77) = 116 + 1 + 60 = 177; etc.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..50
Crossrefs
Programs
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Maple
with(numtheory); P:=proc(q) local a, b, i; global n; for n from 1 to q do for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i; if a>0 and b>0 then if phi(n)+phi(a)+phi(b)=n then print(n); break; fi; fi; od; od; end: P(10^9);
Extensions
a(18) inserted by Giovanni Resta, May 27 2015