

A072278


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


2



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
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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 A280316 A131538
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



