login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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