cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A348034 Numbers k that have at least one unitary divisor d such that sigma(d)*d is equal to k.

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%I A348034 #12 Sep 28 2021 08:35:17
%S A348034 1,6,12,28,30,56,117,120,132,182,306,380,496,552,672,775,870,992,1080,
%T A348034 1406,1680,1722,1892,2016,2184,2256,2793,2862,3276,3540,3782,3960,
%U A348034 4556,4560,4650,5112,5402,5460,6320,6552,6972,7392,8010,8128,9180,9300,9506,9801,10302,10712,11556,11904,11990,12882,16093,16256
%N A348034 Numbers k that have at least one unitary divisor d such that sigma(d)*d is equal to k.
%H A348034 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A348034 120 = 2^3 * 3 * 5 has a unitary divisor 8 for which sigma(8) = 15 = 120/8, thus 120 is included in the sequence.
%e A348034 672 = 2^5 * 3 * 7 has a unitary divisor 21 for which sigma(21) = 32 = 120/21, thus 672 is included in the sequence.
%t A348034 q[n_] := DivisorSum[n, 1 &, CoprimeQ[#, n/#] && #*DivisorSigma[1, #] == n &] > 0; Select[Range[16256], q] (* _Amiram Eldar_, Sep 27 2021 *)
%o A348034 (PARI) isA348034(n) = { fordiv(n, d, if(1==gcd(d,n/d)&&n==d*sigma(d),return(1))); (0); };
%Y A348034 Subsequence of A327165. Even terms of A000396 are all present.
%Y A348034 Positions of nonzero terms in A348033.
%Y A348034 Cf. also A348035 (multiply-perfect numbers in this sequence).
%K A348034 nonn
%O A348034 1,2
%A A348034 _Antti Karttunen_, Sep 26 2021