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A144695 Numbers n such that sigma_1(n)/sigma_0(n) = c^2, c an integer. 5

%I

%S 1,7,17,22,30,31,71,94,97,115,119,127,138,154,164,165,199,210,214,217,

%T 241,260,265,318,337,343,374,382,449,497,510,513,517,527,577,647,658,

%U 668,679,682,705,745,759,805,862,881,889,894,930,966,967,996,1102,1125

%N Numbers n such that sigma_1(n)/sigma_0(n) = c^2, c an integer.

%C A000203(n)/A000005(n) = c^2. Generalized sigma-sequences are sequences of numbers n for which sigma_r(n)/sigma_s(n) = c^t . Sigma_i(n) denotes sum of i-th powers of divisors of n; c,r,s,t positive integers. This sequence has r=1,s=0,t=2, sequence A003601 has r=1,s=0,t=1, sequence {1,21,53,85,102,110,127,217,431,....} has r=1,s=0,t=3, sequence A020487 has r=2,s=1,t=1, sequence A020486 has r=2,s=0,t=1, sequence A140480 has r=2,s=0,t=2.

%H Amiram Eldar, <a href="/A144695/b144695.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor function</a>

%p A000005 := proc(n) numtheory[tau](n) ; end: A000203 := proc(n) numtheory[sigma](n) ; end: isA144695 := proc(n) local s ; s := A000005(n) ; if s <> 0 then issqr(A000203(n)/s) ; else false ; fi; end: for n from 1 to 5000 do if isA144695(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Sep 20 2008

%t Select[Range[1125], IntegerQ @ Sqrt[DivisorSigma[1, #]/DivisorSigma[0, #]] &] (* _Amiram Eldar_, Nov 20 2019 *)

%Y Cf. A000005, A000203, A140480, A003601, A020487, A020486.

%K easy,nonn

%O 1,2

%A _Ctibor O. Zizka_, Sep 19 2008

%E More terms from _R. J. Mathar_, Sep 20 2008

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)