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.
%I A379490 #18 Aug 19 2025 09:32:52
%S A379490 399736269009,1013616036225,1393148751631700625,
%T A379490 2998748839068013955625,3547850289210724050225
%N A379490 Odd squares s such that 2*s is equal to bitwise-AND of 2*s and sigma(s).
%C A379490 If there are any quasiperfect numbers, i.e., numbers x for which sigma(x) = 2*x+1, then they should occur also in this sequence.
%C A379490 Square roots of these terms are: 632247, 1006785, 1180317225, 54760833075, 59563833735.
%C A379490 Question: Are there any solutions to similar equations "Odd squares s such that 2*s is equal to bitwise-AND of 2*s and A001065(s)" and "Odd squares s such that 3*s is equal to bitwise-AND of 3*s and sigma(s)"? Such sequences would contain odd triperfect numbers, if they exist (cf. A005820, A347391, A347884). - _Antti Karttunen_, Aug 19 2025
%C A379490 a(6) > 4*10^21. - _Giovanni Resta_, Aug 19 2025
%H A379490 Paolo Cattaneo, <a href="http://www.bdim.eu/item?fmt=pdf&id=BUMI_1951_3_6_1_59_0">Sui numeri quasiperfetti</a>, Bollettino dell’Unione Matematica Italiana, Serie 3, Vol.6(1951), n.1, p. 59-62.
%H A379490 P. Hagis and G. L. Cohen, <a href="http://dx.doi.org/10.1017/S1446788700018401">Some Results Concerning Quasiperfect Numbers</a>, J. Austral. Math. Soc. Ser. A 33, 275-286, 1982.
%H A379490 V. Siva Rama Prasad and C. Sunitha, <a href="http://nntdm.net/papers/nntdm-23/NNTDM-23-3-073-078.pdf">On quasiperfect numbers</a>, Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 3, 73-78.
%o A379490 (PARI) k=0; forstep(n=1,oo,2, if(!((n-1)%(2^27)),print1("("n")")); if(!isprime(n) && omega(n)>=3, f = factor(n); sq=n^2; sig=prod(i=1,#f~,((f[i,1]^(1+(2*f[i,2])))-1) / (f[i,1]-1)); if(((2*sq)==bitand(2*sq, sig)), k++; print1(sq,", "))));
%Y A379490 Odd squares in A324647.
%Y A379490 Intersection of A016754 and A324647.
%Y A379490 Subsequence of A325311, which is a subsequence of A005231.
%Y A379490 Cf. A000203, A001065, A004198, A318468.
%Y A379490 Cf. also A336700, A336701, A337339, A337342, A348742, A379474, A379503, A379505, A379949 for other conditions that quasiperfect numbers should satisfy.
%K A379490 nonn,more
%O A379490 1,1
%A A379490 _Antti Karttunen_, Jan 13 2025
%E A379490 a(4) and a(5) from _Giovanni Resta_, Aug 19 2025