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A272981 Least prime k>1 such that the sum of divisors of powers k^e, 1 <= e <= n, are divisible by the number their divisors, d(k^e). 3
3, 7, 7, 31, 31, 211, 211, 211, 211, 2311, 2311, 120121, 120121, 120121, 120121, 4084081, 4084081, 106696591, 106696591, 106696591, 106696591, 892371481, 892371481, 892371481, 892371481, 892371481, 892371481, 71166625531, 71166625531, 200560490131, 200560490131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For 1<n<11 A272981(n) = A092967(n+1).

The different numbers are listed in A073917.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..100

EXAMPLE

sigma(3) / d(3) = 4 / 2 = 2 but sigma(3^2) / d(3^2) = 13 / 3;

sigma(7) / d(7) = 8 / 2 = 4, sigma(7^2) / d(7^2) = 57 / 3 = 19, sigma(7^3) / d(7^3) = 400 / 4 = 100 but sigma(7^4) / d(7^4) = 2801 / 5.

MAPLE

with(numtheory): P:= proc(q) local a, j, k, ok, p; global n; a:=2;

for k from 1 to q do for n from a to q do ok:=1;

for j from 1 to k do if not type(sigma(n^j)/tau(n^j), integer) then ok:=0; break; fi; od;

if ok=1 then a:=n; print(n); break; fi; od; od; end: P(10^9);

MATHEMATICA

Table[SelectFirst[Range[2, 10^6], AllTrue[#^Range@ n, Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] &], {n, 15}] (* Michael De Vlieger, May 12 2016, Version 10 *)

CROSSREFS

Cf. A000005, A000203, A073917, A092967, A272980.

Sequence in context: A184467 A004794 A336719 * A086839 A316258 A258405

Adjacent sequences:  A272978 A272979 A272980 * A272982 A272983 A272984

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 12 2016

STATUS

approved

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Last modified June 14 08:31 EDT 2021. Contains 345018 sequences. (Running on oeis4.)