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A353061 Zumkeller numbers (A083207) that are not practical numbers (A005153).

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%I A353061 #17 Mar 25 2023 05:28:35
%S A353061 70,102,114,138,174,186,222,246,258,282,318,350,354,366,372,402,426,
%T A353061 438,444,474,490,492,498,516,534,550,564,572,582,606,618,636,642,650,
%U A353061 654,678,708,732,762,770,786,804,822,834,836,852,876,894,906,910,940,942,945,948,978,996
%N A353061 Zumkeller numbers (A083207) that are not practical numbers (A005153).
%C A353061 Different from A007621: A007621 contains no odd numbers, while every odd term in A083207 is here. The numbers 738, 748, 774, 846, ... are in A007621 and are not here.
%C A353061 But the subsequence of even terms (A005843 intersect this sequence) is a subsequence of A007621:
%C A353061 - A007621 = A173490 \ A007620;
%C A353061 - A005843 intersect this sequence = (A005843 intersect A083207) \ A005153;
%C A353061 - A083207 is a subsequence of A023196, and every perfect number is practical;
%C A353061 - So, (A005843 intersect A083207) \ A005153 is a subsequence of A173490, and A005153 is a supersequence of A007620.
%H A353061 Amiram Eldar, <a href="/A353061/b353061.txt">Table of n, a(n) for n = 1..10000</a>
%e A353061 70 is a term since 70 is a Zumkeller number but not a practical number: 1+5+7+10+14+35 = 2+70, so 70 is a Zumkeller number; but 4 cannot be written as a sum of distinct divisors of 70, so 70 is not practical.
%o A353061 (PARI) isA353061(n) = is(n) && !is_A005153(n) \\ See A083207 for is(n) and A005153 for is_A005153(n)
%Y A353061 Cf. A083207, A005153, A007621.
%Y A353061 Cf. also A173490, A007620, A023196, A005843.
%K A353061 nonn
%O A353061 1,1
%A A353061 _Jianing Song_, Apr 20 2022