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.

80, 880, 1920, 3140, 3880, 7305, 8080, 57755, 63405, 88880, 193920, 1188031, 1226221, 1794971, 7966197, 8339125

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

Table of n, a(n) for n=1..16.

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