A325379 - OEIS

%I #15 Apr 22 2019 13:50:41

%S 12,52,72,148,132,216,172,192,84,292,252,292,412,476,352,520,432,640,

%T 592,472,492,672,532,552,748,412,672,976,732,576,772,1132,1048,1128,

%U 852,1284,892,952,972,1324,1460,1356,1624,1720,1132,1152,1192,-36,1660,1272,1068,1332,1812,1372,1888,1392,2116,1452,1972,2040,1552,2116

%N a(n) = A033879(A228058(n)).

%C The negative terms -36, -1692, -2388, -34944, -16596, -38628, -512, ..., occur at n = 48, 378, 1744, 2255, 2745, 2870, 3555, ..., where A228058(n) is 2205, 19845, 108045, 143325, 178605, 187425, 236925, ..., one of the odd abundant numbers, A005231.

%H Antti Karttunen, <a href="/A325379/b325379.txt">Table of n, a(n) for n = 1..25000</a>

%F a(n) = A033879(A228058(n)).

%F a(n) = A325319(n) - A325320(n).

%F A001511(abs(a(n))) = A325310(A228058(n)), assuming there are no odd perfect numbers, in which case A001511(abs(a(n))) >= 3 for all n. That is, all terms are multiples of 4.

%o (PARI)

%o A033879(n) = (n+n-sigma(n));

%o isA228058(n) = if(!(n%2)||(omega(n)<2),0,my(f=factor(n),y=0); for(i=1,#f~,if(1==(f[i,2]%4), if((1==y)||(1!=(f[i,1]%4)),return(0),y=1), if(f[i,2]%2, return(0)))); (y));

%o k=0; n=0; while(k<100,n++; if(isA228058(n), k++; print1(A033879(n), ", ")));

%Y Cf. A005231, A033879, A228058, A228059, A325310, A325319, A325320, A325378.

%K sign

%O 1,1

%A _Antti Karttunen_, Apr 22 2019