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URL: https://oeis.org/A334528

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A334528
Palindromic numbers that are also Niven numbers and Smith numbers.
2
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
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, May 05 2020
STATUS
approved