A284498 a(n) is the least number such that sigma(a(n)) = sigma(R(a(n)))/n, where R(n) is the digit reverse of n and sigma(n) is the sum of the divisors of n.

1, 16, 15, 17, 2178, 299, 129, 110959, 116509, 1001159

Offset

1,2

Comments

a(11) > 10^9. - Giovanni Resta, Mar 29 2017

Links

Table of n, a(n) for n=1..10.

Formula

Solutions of the equation A000203(n) = A000203(A004086(n))/n.

Example

sigma(1) = 1. Its digit reverse is again 1 and sigma(1) = 1 = 1 * 1;
sigma(16) = 31 and sigma(61) = 62 = 2 * 31;
sigma(15) = 24 and sigma(51) = 72 = 3 * 24;
sigma(17) = 18 and sigma(71) = 72 = 4 * 18; etc.

Maple

with(numtheory): R:=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 k, n; for k from 1 to q do for n from 1 to q do
if k*sigma(n)=sigma(R(n)) then print(n); break; fi; od; od; end: P(10^9);

Mathematica

rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; s[n_] := DivisorSigma[1, n]; a[n_] := Block[{k, v}, For[k = 1, Mod[v = s@rev@k, n] > 0 || v != n s@k, k++]; k]; Array[a, 10] (* Giovanni Resta, Mar 29 2017 *)

Crossrefs

Cf. A000203, A004086, A284495 - A284497.

Sequence in context: A070541 A022972 A023458 * A070576 A173778 A103908

Adjacent sequences: A284495 A284496 A284497 * A284499 A284500 A284501

Keyword

nonn,more,base

Author

Paolo P. Lava, Mar 28 2017

Status

approved