A254320 Numbers k such that the reversal of phi(k) is sigma(k)-k.

2, 11, 101, 735, 7665, 11505, 16459, 64578, 378871, 541033, 3440409, 5639353, 5230000213, 5762782573, 5828558173, 8130408803, 8275586723, 9738107377, 11263073973, 37057275961, 38914628453, 58285958173, 231243884637, 350649946051, 380047486211, 516420024613, 547083380743, 576216622573

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Example

sigma(2) - 2 = 1; rev(1) = 1 = phi(2).
sigma(735) - 735 = 633; rev(633) = 336 = phi(735).

Maple

with(numtheory):T:=proc(w) local x, y, z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
P:=proc(q) local n; for n from 1 to q do
if T(phi(n))=sigma(n)-n then print(n); fi; od; end: P(10^7);

Mathematica

Select[Range[564*10^4], IntegerReverse[EulerPhi[#]]==DivisorSigma[1, #]-#&] (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jul 03 2024 *)

Prog

(PARI) rev(n) = subst(Polrev(digits(n)), x, 10);
isok(n) = (sigma(n)-n) == rev(eulerphi(n)); \\ Michel Marcus, Jan 29 2015

Crossrefs

Cf. A000010, A000203, A001065, A069225, A247080.

Sequence in context: A090726 A036953 A368879 * A115062 A062397 A158578

Adjacent sequences: A254317 A254318 A254319 * A254321 A254322 A254323

Keyword

nonn,base,changed

Author

Paolo P. Lava, Jan 28 2015

Extensions

a(12) from Michel Marcus, Jan 29 2015

a(13)-a(28) from Giovanni Resta, May 08 2015

Status

approved