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

Author

Paolo P. Lava, Oct 01 2014

Keywords

• nonn
• base
• more

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

Examples

			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.
		

Crossrefs

Cf. A000010, A004086, A062687, A247826.

Programs

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);

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

Extensions

a(11)-a(16) from Michel Marcus, Oct 10 2014

Name clarified and a(17)-a(22) from Jinyuan Wang, Apr 08 2025