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

1,1

Comments

In general Sum_{d|k} phi(d) = k.

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..22.

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, A004086, A062687, A247826.

Sequence in context: A386783 A200550 A052519 * A198400 A182680 A203347

Adjacent sequences: A246542 A246543 A246544 * A246546 A246547 A246548

Keyword

nonn,base,more

Author

Paolo P. Lava, Oct 01 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

Status

approved