A072278 Numbers n such that phi(n) is the sum of the first k divisors of n for some k.

1, 2, 18, 42, 48, 72, 152, 210, 378, 462, 765, 1242, 1440, 2080, 2528, 2604, 4480, 6336, 8720, 17248, 17664, 21800, 45675, 84456, 106272, 122220, 318400, 344400, 532016, 654848, 1002456, 1707840, 1904640, 4355190, 5688540, 6600128, 7985628

Offset

1,2

Comments

The majority are congruent to 0 modulo 6.

29292581888, 38187663360, 97473314304, 114918027264, 147840201728 and 208686261248 are also terms. - Donovan Johnson, Aug 30 2011

Links

Giovanni Resta, Table of n, a(n) for n = 1..66 (terms < 10^11, first 60 terms from Donovan Johnson)

Example

The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. phi(72) = 24 = 1 + 2 + 3 + 4 + 6 + 8; hence 72 belongs to the sequence.

Mathematica

Select[Range[10000], MemberQ[FoldList[Plus, 0, Divisors[#]], EulerPhi[#]] &] (* T. D. Noe, Aug 29 2011 *)
Select[Range[8*10^6], MemberQ[Accumulate[Divisors[#]], EulerPhi[#]]&] (* Harvey P. Dale, Nov 11 2014 *)

Crossrefs

Sequence in context: A050594 A098857 A189333 * A296266 A365493 A280316

Adjacent sequences: A072275 A072276 A072277 * A072279 A072280 A072281

Keyword

nonn

Author

Joseph L. Pe, Jul 09 2002

Extensions

Edited and extended by Robert G. Wilson v, Jul 15 2002

Status

approved