A332229 - OEIS

%I #11 Feb 13 2020 20:16:29

%S 290,434,550,826,858,1394,1798,2254,2418,2546,2950,3094,3910,4150,

%T 4382,4930,5590,6138,6358,6390,6710,6966,7514,7546,7622,7658,7990,

%U 8550,8798,8906,9230

%N Even numbers k such that A156552(k) is not a power of prime, and for which A323243(k) = sigma(A156552(k)) is congruent to 2 modulo 8.

%C Numbers k for which A156552(k) is in A332228.

%C Sequence A005940(1+A332228(n)), n >= 1, sorted into ascending order.

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%o (PARI)

%o A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552

%o isA332228(n) = ((n%2)&&!isprimepower(n)&&2==(sigma(n)%8));

%o isA332229(n) = isA332228(A156552(n));

%o (PARI)

%o v156552sigs = readvec("a156552.txt"); \\ Factorization file for A156552 prepared by Hans Havermann, available at https://oeis.org/A156552/a156552.txt

%o isA156552not_a_primepower(n) = if(n<=2,0,my(prsig=v156552sigs[n]); length(prsig[1])>1);

%o A323243(n) = if(n<=2,n-1,my(prsig=v156552sigs[n],ps=prsig[1],es=prsig[2]); prod(i=1,#ps,((ps[i]^(1+es[i]))-1)/(ps[i]-1)));

%o isA332229(n) = (!(n%2)&&isA156552not_a_primepower(n)&&(2==(A323243(n)%8)));

%o k=0; for(n=1,10000,if(isA332229(n),k++; print1(n,", ")));

%Y Cf. A000203, A005940, A156552, A323243, A332225, A332228.

%Y Subsequence of A324814.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 13 2020