A246545 Numbers k with at least one nonpalindromic divisor such that the sum of phi(d) = the sum of phi(reverse(d)), where d runs over the divisors of k and phi is the Euler totient function.
80, 880, 1920, 3140, 3880, 7305, 8080, 57755, 63405, 88880, 193920, 1188031, 1226221, 1794971, 7966197, 8339125, 13488431, 63007844, 123848321, 165387961, 312256913, 698621186
Offset: 1
Examples
Divisors of 3140 are 1, 2, 4, 5, 10, 20, 157, 314, 628, 785, 1570, 3140. Adding the Euler totient function of the reverse of the divisors: phi(1) + phi(2) + phi(4) + phi(5) + phi(01) + phi(02) + phi(751) + phi(413) + phi(826) + phi(587) + phi(0751) + phi(0413) = 3140.
Programs
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Maple
with(numtheory); T:=proc(h) local x,y,w; x:=h; y:=0; for w from 1 to ilog10(h)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end: P:=proc(q) local a,b,k,n,ok; for n from 1 to q do a:=divisors(n); b:=0; ok:=0; for k from 1 to nops(a) do b:=b+phi(T(a[k])); if a[k]<>T(a[k]) then ok:=1; fi; od; if ok=1 and n=b then print(n); fi; od; end: P(10^9);
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PARI
isok(n) = {d = divisors(n); rd = vector(#d, i, subst(Polrev(digits(d[i])), x, 10)); (d != rd) && (n == sum(i=1, #rd, eulerphi(rd[i])));} \\ Michel Marcus, Oct 10 2014
Extensions
a(11)-a(16) from Michel Marcus, Oct 10 2014
Name clarified and a(17)-a(22) from Jinyuan Wang, Apr 08 2025
Comments