login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A051281 Sum of divisors of n, sigma(n) (A000203), is a power of number of divisors of n, d(n) (A000005). 7
1, 3, 7, 31, 127, 217, 889, 2667, 3937, 8191, 27559, 57337, 131071, 172011, 253921, 524287, 917497, 1040257, 1777447, 3670009, 4063201, 11010027, 12189603, 16252897, 16646017, 66584449, 113770279, 116522119, 225735769, 677207307, 1073602561, 2147483647, 3612185689, 4294434817, 7515217927 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All Mersenne primes (A000668) are terms.

Subsequence of A046528 (product of distinct Mersenne primes). - Michel Marcus, Feb 15 2020

LINKS

David A. Corneth, Table of n, a(n) for n = 1..2000

EXAMPLE

d(217) = 4; sigma(217) = 256 = 4^4.

MATHEMATICA

spdQ[n_]:=Module[{sd=DivisorSigma[1, n], nd=DivisorSigma[0, n]}, sd == nd^IntegerExponent[sd, nd]]; Join[{1}, Select[Range[2, 226000000], spdQ]] (* Harvey P. Dale, May 02 2012 *)

PROG

(PARI) is(n)=my(t, e=ispower(sigma(n), , &t)); if(!e, return(n==1), nd); nd=numdiv(n); fordiv(e, d, if(t^d==nd, return(1))); 0 \\ Charles R Greathouse IV, Feb 19 2013

(PARI) isA051281(n) = { if(n==1, return(1)); my(sig = sigma(n), ndiv = numdiv(n), v = valuation(sig, ndiv)); (ndiv^v == sig); } \\ Antti Karttunen, Jun 30 2017

CROSSREFS

Cf. A000005, A000203, A046528, A286628, A289276.

Sequence in context: A003260 A152058 A138865 * A145038 A138864 A105768

Adjacent sequences:  A051278 A051279 A051280 * A051282 A051283 A051284

KEYWORD

nonn,nice

AUTHOR

Michel ten Voorde

EXTENSIONS

More terms from Jud McCranie

a(30)-a(32) from Donovan Johnson, Oct 03 2012

a(33)-a(35) from Michel Marcus, Feb 14 2020

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 21 02:29 EDT 2020. Contains 337266 sequences. (Running on oeis4.)