|
|
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
|
|
|
KEYWORD
|
nonn,more,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|