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A284496
a(n) is the least number such that bigomega(a(n)) = bigomega(R(a(n)))/n, where R(n) is the digit reverse of n and bigomega(n) is the number of prime divisors of n counted with multiplicity.
2
2, 19, 29, 61, 23, 487, 821, 2557, 2749, 4201, 25747, 61843, 211643, 614881, 238673, 272059, 270131, 405719, 8239969, 42037283, 44922991, 44166589, 67719697, 61277761, 253442899, 2321783617, 4471131827, 4640384471, 40782386369, 4055086219, 25135138387, 63558323051
OFFSET
1,1
COMMENTS
All values are prime.
FORMULA
Solutions of the equation A001222(n) = A001222(A004086(n))/n.
EXAMPLE
bigomega(2) = 1. Its digit reverse is again 2 and bigomega(2) = 1 = 1 * 1;
bigomega(19) = 1 and bigomega(91) = 2 = 2 * 1;
bigomega(29) = 1 and bigomega(92) = 3 = 3 * 1;
bigomega(61) = 1 and bigomega(16) = 4 = 4 * 1; 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*bigomega(n)=bigomega(R(n)) then print(n); break; fi; od; od; end: P(10^9);
MATHEMATICA
rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; a[n_] := Block[{k, v}, For[k=2, Mod[v = PrimeOmega@ rev@ k, n] > 0 || v != n PrimeOmega@ k, k++]; k]; Array[a, 12] (* Giovanni Resta, Mar 29 2017 *)
PROG
(PARI) genit(maxx)={for(num=1, maxx, soln=0; forprime(p=2, 9E20, f=Vecrev(Str(p)); g=eval(concat(f)); if(bigomega(g)==num, print(num, " ", p); soln=1; break)); if(soln<1, print("increase max prime"))); } \\ Bill McEachen, Mar 30 2017
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Mar 28 2017
EXTENSIONS
a(23)-a(32) from Giovanni Resta, Mar 29 2017
a(26) corrected by Bill McEachen, Mar 30 2017
STATUS
approved