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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304294 Numbers k having at least one divisor d such that sigma(k) = sigma(k+d). 1
14, 54, 154, 182, 206, 220, 238, 264, 266, 270, 284, 322, 366, 406, 434, 518, 574, 594, 602, 658, 660, 702, 742, 826, 834, 848, 852, 854, 918, 938, 957, 994, 1022, 1026, 1030, 1106, 1162, 1240, 1242, 1246, 1334, 1350, 1358, 1364, 1392, 1414, 1420, 1442, 1498, 1504 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first number that admits two different divisors is 702: two of its divisors are 6 and 26, and sigma(702) = sigma(702 + 6) = sigma(702 + 26) = 1680.

The first number that admits three different divisors is 11934: three of its divisors are 26, 102, and 442, and sigma(11934) = sigma(11934 + 26) = sigma(11934 + 102) = sigma(11934 + 442) = 30240.

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

One divisor of 14 is 1 and sigma(14) = sigma(14 + 1) = 24.

One divisor of 54 is 2 and sigma(54) = sigma(54 + 2) = 120.

MAPLE

with(numtheory): P:=proc(n) local a, k, ok; a:=divisors(n); ok:=0;

for k from 1 to nops(a) do if sigma(n)=sigma(n+a[k]) then ok:=1; fi; od;

if ok=1 then n; fi; end: seq(P(i), i=1..1504);

MATHEMATICA

Select[Range[2000], Function[k, AnyTrue[Divisors@ k, DivisorSigma[1, k] == DivisorSigma[1, k + #] &]]] (* Michael De Vlieger, May 14 2018 *)

PROG

(PARI) isok(n) = sumdiv(n, d, sigma(n+d) == sigma(n)) > 0; \\ Michel Marcus, May 14 2018

CROSSREFS

Cf. A000203, A304295.

Sequence in context: A048971 A299646 A006597 * A114012 A140784 A022285

Adjacent sequences:  A304291 A304292 A304293 * A304295 A304296 A304297

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava, May 14 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 December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)