A180097 - OEIS

A180097

Numbers k such that sigma(k) is powerful.

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, 381, 382, 385, 391, 400, 426, 431, 462, 470, 472, 497, 499

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OFFSET

1,2

COMMENTS

Numbers k such that A000203(k) = A387726(k). - Antti Karttunen, Sep 12 2025

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, A387726.

Subsequence of A387727.

Sequence in context: A196035 A196038 A387727 * 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

More terms added (to differentiate from A387727) by Antti Karttunen, Sep 12 2025

STATUS

approved