A253968
Numbers n such that (23*10^n - 26)/6 is prime.
Original entry on oeis.org
2, 4, 6, 10, 11, 18, 29, 151, 920, 1456, 1716, 1915, 4148, 4403, 8005, 9600, 41945, 47238
Offset: 1
n = 2, 4, and 6, yield (23*10^n - 26)/6 = 379, 38329, and 3833329, respectively, which are prime.
A254004
Numbers that divide the reverse of the sum of their divisors.
Original entry on oeis.org
1, 14, 69, 102, 123, 134, 164, 276, 639, 2556, 9568, 1259196, 1333334, 1473381, 1741983, 133333334, 821554911, 929247534, 1333333334, 22214600673, 133333333334
Offset: 1
sigma(14) = 24, Rev(24) = 42 and 42 / 14 = 3.
sigma(69) = 96, Rev(96) = 69 and 69 / 69 = 1.
sigma(9568) = 21168, Rev(21168) = 86112 and 86112 / 9568 = 9.
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[n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)))) mod n eq 0]; // Bruno Berselli, Jan 22 2015
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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 type(T(sigma(n))/n,integer) then print(n);
fi; od; end: P(10^9);
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Select[Range@ 2000000, Mod[FromDigits@ Reverse@ IntegerDigits@ DivisorSigma[1, #], #] == 0 &] (* Michael De Vlieger, May 09 2015 *)
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isok(n) = !(eval(concat(Vecrev(Str(sigma(n))))) % n); \\ Michel Marcus, Feb 27 2015
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