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 A246545 Numbers such that Sum_{i=1..k}{phi(d(i))} = Sum_{i=1..k}{phi(Rev(d(i)))}, where d(i) are the k divisors of n, Rev(d(i)) the reverse of the divisors d(i) and phi(x) the Euler totient function. Numbers with all palindromic divisors are not considered. 1
 80, 880, 1920, 3140, 3880, 7305, 8080, 57755, 63405, 88880, 193920, 1188031, 1226221, 1794971, 7966197, 8339125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In general Sum_{i=1..k}{phi(d(i))} = n, where d(i) are the k divisors of n. The numbers that are not considered here belong to A062687, numbers all of whose divisors are palindromic. - Michel Marcus, Oct 10 2014 LINKS EXAMPLE 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. 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); PROG (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 CROSSREFS Cf. A000010, A196677, A247826. Sequence in context: A024392 A200550 A052519 * A198400 A182680 A203347 Adjacent sequences:  A246542 A246543 A246544 * A246546 A246547 A246548 KEYWORD nonn,more,base AUTHOR Paolo P. Lava, Oct 01 2014 EXTENSIONS a(11)-a(16) from Michel Marcus, Oct 10 2014 STATUS approved

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Last modified August 9 03:22 EDT 2022. Contains 356016 sequences. (Running on oeis4.)