A334528 Palindromic numbers that are also Niven numbers and Smith numbers.

4, 666, 28182, 45054, 51315, 82628, 239932, 454454, 864468, 2594952, 2976792, 3189813, 3355533, 4172714, 4890984, 5319135, 5367635, 5777775, 7149417, 7247427, 8068608, 8079708, 8100018, 8280828, 8627268, 9227229, 9423249, 21699612, 22544522, 24166142, 27677672

Offset

1,1

Comments

Witno (2014) proved that this sequence is infinite.

Links

Amiram Eldar, Table of n, a(n) for n = 1..512

Amin Witno, Smith Numbers With Extra Digital Features, Integers, Vol. 14 (2014), Article A66.

Example

666 is a term since it is palindromic, a Niven number (6 + 6 + 6 = 18 is a divisor of 666) and a Smith number (666 = 2 * 3 * 3 * 37 and 6 + 6 + 6 = 2 + 3 + 3 + 3 + 7).

Mathematica

digSum[n_] := Plus @@ IntegerDigits[n]; palNivenSmithQ[n_] := PalindromeQ[n] && Divisible[n, (ds = digSum[n])] && CompositeQ[n] && Plus @@ (Last@# * digSum[First@#] & /@ FactorInteger[n]) == ds; Select[Range[10^5], palNivenSmithQ]

Crossrefs

Intersection of A002113, A005349 and A006753.

Intersection of any two of the sequences A082232, A098834 and A334527.

Sequence in context: A067171 A046348 A332164 * A183150 A202368 A114765

Adjacent sequences: A334525 A334526 A334527 * A334529 A334530 A334531

Keyword

nonn,base

Author

Amiram Eldar, May 05 2020

Status

approved