cp's OEIS Frontend

A280354 Numbers n such that (i) number of divisors of n equals number of divisors of digit reversal of n, (ii) sum of divisors of n equals sum of divisors of digit reversal of n, and (iii) n is not a palindrome.

%I A280354 #20 Dec 17 2024 19:14:58
%S A280354 1561,1651,5346,6435,157661,166751,301134,321853,358123,431103,507955,
%T A280354 511665,517055,537495,539946,550715,559705,566115,576908,594735,
%U A280354 649935,729287,765677,776567,782927,809675,834498,894438,896898,898698,905289,982509,1257912,1473302
%N A280354 Numbers n such that (i) number of divisors of n equals number of divisors of digit reversal of n, (ii) sum of divisors of n equals sum of divisors of digit reversal of n, and (iii) n is not a palindrome.
%C A280354 Intersection of A062895 and A085329.
%C A280354 Numbers n such that A000005(n) = A000005(A004086(n)), A000203(n) = A000203(A004086(n)) and A136522(n) = 0.
%H A280354 Indranil Ghosh, <a href="/A280354/b280354.txt">Table of n, a(n) for n = 1..200</a>
%H A280354 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%e A280354 1561 is in the sequence because 1561 has 4 divisors {1, 7, 223, 1561}, 1 + 7 + 223 + 1561 = 1792 and 1651 has 4 divisors {1, 13, 127, 1651}, 1 + 13 + 127 + 1651 = 1792.
%t A280354 Select[Range[1500000], !PalindromeQ[#1] && DivisorSigma[0, #1] == DivisorSigma[0, FromDigits[Reverse[IntegerDigits[#1]]]] && DivisorSigma[1, #1] == DivisorSigma[1,FromDigits[Reverse[IntegerDigits[#1]]]] & ]
%t A280354 fQ[n_]:=With[{irn=IntegerReverse[n]},!PalindromeQ[n]&&DivisorSigma[0,n]==DivisorSigma[0,irn] && DivisorSigma[1,n] == DivisorSigma[ 1,irn]]; Select[Range[1480000],fQ] (* _Harvey P. Dale_, Dec 17 2024 *)
%o A280354 (PARI) R(n) = eval(concat(Vecrev(Str(n))));
%o A280354 isok(n) = n != R(n) && numdiv(n) == numdiv(R(n)) && sigma(n) == sigma(R(n));
%o A280354 for(n=1561, 1473302, if(isok(n), print1(n, ", "))) \\ _Indranil Ghosh_, Mar 06 2017
%Y A280354 Cf. A000005, A000203, A004086, A029742, A062895, A085329, A136522.
%K A280354 nonn,base
%O A280354 1,1
%A A280354 _Ilya Gutkovskiy_, Jan 01 2017