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

Author

Amiram Eldar, May 05 2020

Keywords

• nonn
• base

Comments

Witno (2014) proved that this sequence is infinite.

Examples

			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).
		

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.

Crossrefs

Intersection of A002113, A005349 and A006753.

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

Programs

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]