A359331 Nonprime numbers k for which k*k' is a palindrome, where k' is the arithmetic derivative of k (A003415).

1, 34, 44, 49, 121, 476, 524, 533, 1808, 6797, 7326, 10016, 10201, 10403, 10817, 16019, 17831, 26322, 33898, 55198, 57247, 74711, 87241, 131395, 148753, 156029, 239593, 240021, 289831, 295022, 423758, 441691, 595777, 725754, 900009, 2568543, 2910271, 2981619

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Example

1*1' = 1*0 = 0, so 1 is a term.
34*34' = 34*19 = 646, so 34 is a term.
49*49' = 49*14 = 686, so 49 is a term.

Maple

d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
q:= n-> not isprime(n) and StringTools[IsPalindrome](""||(n*d(n))):
select(q, [$1..3000000])[];  # Alois P. Heinz, Jan 29 2023

Mathematica

d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[3*10^6], ! PrimeQ[#] && PalindromeQ[# * d[#]] &] (* Amiram Eldar, Jan 29 2023 *)

Prog

(Magma) f:=func<h |h le 1 select 0 else  h*(&+[Factorisation(h)[i][2] /
Factorisation(h)[i][1]: i in [1..#Factorisation(h)]])>; pal:=func<n|Intseq(n) eq Reverse(Intseq(n))>; [n:n in [1..3000000]|not IsPrime(n) and pal(n*Floor(f(n)))];

Crossrefs

Cf. A002113, A003415, A018252, A190116.

Sequence in context: A044020 A217276 A076772 * A248527 A206262 A302457

Adjacent sequences: A359328 A359329 A359330 * A359332 A359333 A359334

Keyword

nonn,base

Author

Marius A. Burtea, Jan 29 2023

Status

approved