login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304283 Numbers equal to the sum of their aliquot parts, each of them decreased by 6. 8
104704, 407715, 8576892928 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Searched up to n = 10^12.

From Giovanni Resta, May 11 2018: (Start)

If p = 2^(1+t) + (1+2*t)*k - 1 is a prime, for some t > 0 and k even, then x = 2^t*p is in the sequence where k is the value by which the sum of aliquot parts is increased.

In this sequence k = -6; for t = 24 we get 562945004142592, which is a term greater than 8576892928, but this does not exclude the existence of other intermediate terms following a different solution pattern. (End)

Terms using odd values of k seem very hard to find. Up to n = 10^12, only three such terms are known: 2, 98, and 8450, for k = 1, 5, and -7, respectively.

LINKS

Table of n, a(n) for n=1..3.

EXAMPLE

Aliquot parts of 104704 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 409, 818, 1636, 3272, 6544, 13088, 26176, 52352 and (1-6) + (2-6) + (4-6) + (8-6) + (16-6) + (32-6) + (64-6) + (128-6) + (256-6) + (409-6) + (818-6) + (1636-6) + (3272-6) + (6544-6) + (13088-6) + (26176-6) + (52352-6) + = 104704.

MAPLE

with(numtheory): P:=proc(q, k) local n;

for n from 1 to q do if 2*n=sigma(n)+k*(tau(n)-1) then print(n);

fi; od; end: P(10^12, -6);

MATHEMATICA

With[{k = -6}, Select[Range[10^6], DivisorSum[#, # + k &] - (# + k) == # &] ] (* Michael De Vlieger, May 14 2018 *)

CROSSREFS

Cf. A000005, A000203, A000396, A304276, A304277, A304278, A304279, A304280, A304281, A304282, A304284.

Sequence in context: A106024 A174293 A186877 * A138165 A202934 A203822

Adjacent sequences:  A304280 A304281 A304282 * A304284 A304285 A304286

KEYWORD

nonn,hard,more

AUTHOR

Paolo P. Lava, May 11 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 22 05:47 EDT 2019. Contains 327287 sequences. (Running on oeis4.)