

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
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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



