login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A194196 Numbers k such that the sum of the divisors of k and the sum of the distinct prime divisors of k are both a square. 1
1, 66, 94, 1092, 1146, 1416, 1491, 1782, 2130, 2159, 2805, 3012, 3531, 4836, 8736, 9065, 9911, 12532, 13156, 15960, 16194, 24096, 25866, 27652, 29316, 29484, 30942, 34162, 34782, 34860, 37736, 37884, 38232, 38688, 40257, 41331, 48204, 51460, 54162, 54411 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)

FORMULA

{A006532 intersection A164722}.

EXAMPLE

94 is in the sequence because the distinct prime divisors are {2,47} -> sum = 7^2, and the divisors are {1,2,47,94} -> sum = 12^2.

MAPLE

isA006532 :=proc(n) issqr(numtheory[sigma](n)) ; end proc:

A008472 := proc(n) add(d, d=numtheory[factorset](n)) ; end proc:

isA164722 :=proc(n) issqr(A008472(n)) ; end proc:

for n from 1 to 50000 do if isA006532(n) and isA164722(n) then printf("%d, ", n); end if; end do; # R. J. Mathar, Aug 18 2011

PROG

(PARI) isok(k) = my(f=factor(k)); issquare(sigma(f)) && issquare(vecsum(f[, 1])); \\ Michel Marcus, Dec 05 2020

CROSSREFS

Cf. A000203, A006532, A008472, A164722.

Sequence in context: A031411 A098775 A109759 * A281937 A109141 A031184

Adjacent sequences:  A194193 A194194 A194195 * A194197 A194198 A194199

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 18 2011

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 November 30 08:19 EST 2021. Contains 349419 sequences. (Running on oeis4.)