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.

A194594 Numbers such that the sum of the their nonprime divisors and the sum of their prime divisors are both primes.

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%I A194594 #18 Sep 23 2021 11:15:03
%S A194594 4,6,8,10,12,16,22,27,32,40,44,58,68,80,82,88,116,125,136,164,165,176,
%T A194594 192,232,236,250,256,284,328,352,358,382,420,428,435,462,472,478,486,
%U A194594 512,548,562,640,651,656,665,704,714,764,768,788,798,808,819,838
%N A194594 Numbers such that the sum of the their nonprime divisors and the sum of their prime divisors are both primes.
%H A194594 Amiram Eldar, <a href="/A194594/b194594.txt">Table of n, a(n) for n = 1..10000</a>
%e A194594 The divisors of 136 are { 1, 2, 4, 8, 17, 34, 68, 136 }, the sum of its nonprime divisors is 1 + 4 + 8 + 34 + 68 + 136 = 251 is prime, and the sum of its prime divisors is 2 + 17 = 19 is prime, hence 136 is in the sequence.
%t A194594 f[n_]:=Plus@@Select[Divisors[n],!PrimeQ[#]&];g[n_]:=Plus@@First/@FactorInteger[n];Select[Range[1000],PrimeQ[f[#]&&PrimeQ[g[#]]]&]
%t A194594 ndpdQ[n_]:=Module[{d=Divisors[n],pr},pr=Select[d,PrimeQ];AllTrue[ {Total[ pr],Total[Complement[d,pr]]},PrimeQ]]; Select[Range[900],ndpdQ] (* _Harvey P. Dale_, Sep 23 2021 *)
%o A194594 (PARI) isok(n) = isprime(s=sumdiv(n, d, if (isprime(d), d))) && isprime(sigma(n)-s); \\ _Michel Marcus_, Jan 07 2020
%Y A194594 Cf. A008472, A023890, A194579, A114522.
%K A194594 nonn
%O A194594 1,1
%A A194594 _Michel Lagneau_, Aug 30 2011