cp's OEIS Frontend

A104907 Numbers n such that d(n)*reversal(n)=sigma(n), where d(n) is number of positive divisors of n.

%I A104907 #16 Jan 31 2023 16:38:14
%S A104907 1,73,861,7993,8241,799993,7999993,44908500,82000041,293884500,
%T A104907 6279090751,8200000041,62698513951,79999999993,82000000041,
%U A104907 374665576800,597921764310,7999999999993,8200000000041
%N A104907 Numbers n such that d(n)*reversal(n)=sigma(n), where d(n) is number of positive divisors of n.
%C A104907 All primes of the form 8*10^n-7 are in 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.
%C A104907 a(20) > 10^13. - _Giovanni Resta_, Jul 13 2015
%e A104907 Let p=8*10^n-7 be a prime so d(p)=2; reversal(p)=4*10^n-3 and sigma(p)
%e A104907 =8*10^n-6 hence d(p)*reversal(p)=sigma(p) and this shows that p
%e A104907 is in the sequence. 73,7993,799993 and 7999993 are such terms.
%e A104907 Also let q=(2*10^n+1)/3 be a prime, so 123*q=82*10^n+41; reversal
%e A104907 (123*q)=14*10^n+28; d(123*q)=8 and sigma(123*q)=168*q+168=112*10^n
%e A104907 +224 hence d(123*q)*reversal(123*q)=sigma(123*q) and this shows
%e A104907 that 123*q is in the sequence. 861,8241 and 82000041 are such terms.
%t A104907 reversal[n_]:= FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[0, n]*reversal[n] == DivisorSigma[1, n], Print[n]], {n, 1125000000}]
%t A104907 Select[Range[8*10^6],DivisorSigma[0,#]IntegerReverse[#]==DivisorSigma[1,#]&] (* The program generates the first 7 terms of the sequence. *) (* _Harvey P. Dale_, Jan 31 2023 *)
%Y A104907 Cf. A056657, A093170, A096507, A099190, A105322, A105323, A105324.
%K A104907 base,more,nonn
%O A104907 1,2
%A A104907 _Farideh Firoozbakht_, Apr 16 2005
%E A104907 a(11)-a(15) from _Donovan Johnson_, Feb 06 2010
%E A104907 a(16) from _Giovanni Resta_, Feb 06 2014
%E A104907 a(17)-a(19) from _Giovanni Resta_, Jul 13 2015