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.

1561, 1651, 5346, 6435, 157661, 166751, 301134, 321853, 358123, 431103, 507955, 511665, 517055, 537495, 539946, 550715, 559705, 566115, 576908, 594735, 649935, 729287, 765677, 776567, 782927, 809675, 834498, 894438, 896898, 898698, 905289, 982509, 1257912, 1473302

Offset: 1

Author

Ilya Gutkovskiy, Jan 01 2017

Keywords

• nonn
• base

Comments

Intersection of A062895 and A085329.

Numbers n such that A000005(n) = A000005(A004086(n)), A000203(n) = A000203(A004086(n)) and A136522(n) = 0.

Examples

			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.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..200
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A000005, A000203, A004086, A029742, A062895, A085329, A136522.

Programs

Mathematica

Select[Range[1500000], !PalindromeQ[#1] && DivisorSigma[0, #1] == DivisorSigma[0, FromDigits[Reverse[IntegerDigits[#1]]]] && DivisorSigma[1, #1] == DivisorSigma[1,FromDigits[Reverse[IntegerDigits[#1]]]] & ]
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 *)

PARI

R(n) = eval(concat(Vecrev(Str(n))));
isok(n) = n != R(n) && numdiv(n) == numdiv(R(n)) && sigma(n) == sigma(R(n));
for(n=1561, 1473302, if(isok(n), print1(n, ", "))) \\ Indranil Ghosh, Mar 06 2017