A350533 Happy Niven (or happy harshad) numbers.

1, 7, 10, 70, 100, 133, 190, 192, 230, 280, 320, 392, 440, 644, 700, 736, 820, 874, 888, 910, 912, 1000, 1088, 1090, 1092, 1122, 1125, 1128, 1141, 1148, 1152, 1185, 1188, 1212, 1215, 1233, 1251, 1274, 1275, 1300, 1323, 1330, 1332, 1512, 1521, 1547, 1679, 1725

Offset

1,2

Comments

Numbers that are divisible by the sum of their digits and whose trajectory under iteration of sum of squares of digits map includes 1.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Wikipedia, Happy number

Wikipedia, Harshad number

Formula

{ A005349 } intersect { A007770 }.

Example

133 is a term because 133/7 = 19 and its trajectory under iteration of sum of squares of digits map is 133 -> 19 -> 82 -> 68 -> 100 -> 1.

Maple

q:= proc(n) local m, s; m, s:= n, {};
      if irem(n, add(i, i=convert(n, base, 10)))>0 then return false fi;
      do if m=1 then return true
       elif m in s then return false
       else s, m:= s union {m}, add(i^2, i=convert(m, base, 10))
         fi
      od
    end:
select(q, [$1..2000])[];

Crossrefs

Cf. A003132, A005349, A007770.

Sequence in context: A097187 A115904 A136865 * A351685 A123797 A123805

Adjacent sequences: A350530 A350531 A350532 * A350534 A350535 A350536

Keyword

nonn,base

Author

Alois P. Heinz, Jan 03 2022

Status

approved