login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A093891 Numbers k such that every prime up to sigma(k) is a sum of divisors of k. 6
1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence is infinite as sigma (2^n) = 2^(n+1)-1 and a(2^n) = pi(2^(n+1)-1).

Does this sequence include any non-members of A005153 other than 10, 70 and 836? - Franklin T. Adams-Watters, Apr 28 2006

The answer to the previous comment is yes, this sequence has many terms that are not in A005153. See A174434. - T. D. Noe, Mar 19 2010

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

4 is a member as sigma(4) = 7 and all the primes up to 7 are a partial sum of divisors of 4, since divisors of 4 are 1, 2 and 4 and because primes arising are 2, 3 = 1+2, 5 = 1+4 and 7 = 1+2+4.

MATHEMATICA

Select[Range[240], SubsetQ[Total /@ Rest@ Subsets@ Divisors[#], Prime@ Range@ PrimePi@ DivisorSigma[1, #]] &] (* Michael De Vlieger, Mar 19 2021 *)

PROG

(PARI) isok(m) = {my(d=divisors(m), vp = primes(primepi(sigma(m)))); for (i=1, 2^#d - 1, my(b = Vecrev(binary(i)), x = sum(k=1, #b, b[k]*d[k])); if (vecsearch(vp, x), vp = setminus(vp, Set(x))); if (#vp == 0, return (1)); ); } \\ Michel Marcus, Mar 19 2021

CROSSREFS

Cf. A093890, A093892.

Cf. A005153.

Sequence in context: A114871 A085150 A051178 * A213708 A239063 A151999

Adjacent sequences: A093888 A093889 A093890 * A093892 A093893 A093894

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Apr 23 2004

EXTENSIONS

More terms from Franklin T. Adams-Watters, Apr 28 2006

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 17:49 EST 2022. Contains 358475 sequences. (Running on oeis4.)