

A180097


Numbers n such that sigma(n) is powerful.


3



1, 3, 7, 21, 22, 30, 31, 46, 51, 55, 66, 70, 71, 81, 85, 93, 94, 102, 107, 110, 115, 119, 127, 138, 142, 154, 156, 159, 165, 170, 187, 199, 210, 213, 214, 217, 230, 235, 238, 253, 255, 265, 282, 291, 310, 318, 321, 322, 330, 343, 345, 355, 357, 364, 371, 374
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OFFSET

1,2


LINKS

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


EXAMPLE

sigma(3)=2^2, sigma(7)=2^3, sigma(21)=2^5, sigma(66)=2^4*3^2.


MAPLE

emin := proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z>z[2], L); min(L) else 0 fi end: L:=[]: for w to 1 do for n from 1 to 144 do sn:=numtheory[sigma](n); if emin(sn)>1 then L:=[op(L), n]; print(n, ifactor(n), sn, ifactor(sn)) fi; od; od; L;


MATHEMATICA

sigmaPowerQ[1] = True; sigmaPowerQ[n_] := Min@FactorInteger[DivisorSigma[1, n]][[;; , 2]] > 1; Select[Range[1000], sigmaPowerQ] (* Amiram Eldar, Sep 08 2019 *)


PROG

(PARI) isok(n) = ispowerful(sigma(n)); \\ Michel Marcus, Sep 08 2019


CROSSREFS

Cf. A001694, A000203, A180090, A180098.
Sequence in context: A174348 A196035 A196038 * A065496 A322922 A018479
Adjacent sequences: A180094 A180095 A180096 * A180098 A180099 A180100


KEYWORD

easy,nonn


AUTHOR

Walter Kehowski, Aug 10 2010


EXTENSIONS

a(1) and more terms from Amiram Eldar, Sep 08 2019


STATUS

approved



