1,2

No further term up to 1125*10^6. All primes of the form 8*10^n-7 are the sequence, so 8*10^A099190-3 is a subsequence of this sequence. A105322 is this subsequence. Also if p=(2*10^n+1)/3 is prime then 123*p is in the sequence, so 123*A093170 is a subsequence of this sequence. A105323 is this subsequence.

Let p=8*10^n-7 be a prime so d(p)=2; reversal(p)=4*10^n-3 and sigma(p)

=8*10^n-6 hence d(p)*reversal(p)=sigma(p) and this shows that p

is in the sequence. 73,7993,799993 and 7999993 are such terms.

Also let q=(2*10^n+1)/3 be a prime, so 123*q=82*10^n+41; reversal

(123*q)=14*10^n+28; d(123*q)=8 and sigma(123*q)=168*q+168=112*10^n

+224 hence d(123*q)*reversal(123*q)=sigma(123*q) and this shows

that 123*q is in the sequence. 861,8241 and 82000041 are such terms.

reversal[n_]:= FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[0, n]*reversal[n] == DivisorSigma[1, n], Print[n]], {n, 1125000000}]

Cf. A056657, A093170, A096507, A099190, A105322, A105323, A105324.

Sequence in context: A063784 A066101 A100412 this_sequence A123811 A057522 A008400

Adjacent sequences: A104904 A104905 A104906 this_sequence A104908 A104909 A104910

base,more,nonn

Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Apr 16 2005