[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A284495
a(n) is the least number such that d(a(n)) = d(R(a(n)))/n, where R(n) is the digit reverse of n and d(n) is the number of divisors of n.
3
1, 19, 23, 213, 211, 293, 2519, 827, 2129, 2593, 23259, 2707, 253653, 21143, 21927, 21799, 2177667, 21529, 8239969, 25579, 21757, 232153, 67719697, 210229, 2112597, 2171101, 217519, 211879, 27857904077, 211007, 25135138387, 219059, 2914689, 4878977, 4646637, 230693
OFFSET
1,2
FORMULA
Solutions of the equation A000005(n) = A000005(A004086(n))/n.
EXAMPLE
d(1) = 1. Its digit reverse is again 1 and d(1) = 1 = 1 * 1;
d(19) = 2 and d(91) = 4 = 2 * 2;
d(23) = 2 and d(32) = 6 = 3 * 2;
d(213) = 4 and d(312) = 16 = 4 * 4; 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 2 to q do
if k*tau(n)=tau(R(n)) then print(n); break; fi; od; od; end: P(10^9);
MATHEMATICA
rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; d[n_] := DivisorSigma[0, n]; a[n_] := Block[{k}, For[k=1, d@ rev@ k != n d@ k, k++]; k]; Array[a, 16] (* Giovanni Resta, Mar 29 2017 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Mar 28 2017
EXTENSIONS
a(19)-a(36) from Giovanni Resta, Mar 29 2017
STATUS
approved