A325310 -id:A325310 - cp's OEIS frontend

A325379 a(n) = A033879(A228058(n)).

12, 52, 72, 148, 132, 216, 172, 192, 84, 292, 252, 292, 412, 476, 352, 520, 432, 640, 592, 472, 492, 672, 532, 552, 748, 412, 672, 976, 732, 576, 772, 1132, 1048, 1128, 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

Offset: 1

Antti Karttunen, Apr 22 2019

sign

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.

Antti Karttunen, Table of n, a(n) for n = 1..25000

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

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

a(n) = A033879(A228058(n)).
a(n) = A325319(n) - A325320(n).
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.

A325315 Bitwise-XOR of absolute values of (n - A048250(n)) and (n - A162296(n)).

Original entry on oeis.org

1, 3, 2, 1, 4, 0, 6, 1, 5, 2, 10, 4, 12, 4, 6, 1, 16, 15, 18, 6, 30, 24, 22, 20, 19, 10, 30, 0, 28, 52, 30, 1, 46, 54, 46, 51, 36, 48, 54, 54, 40, 28, 42, 12, 28, 52, 46, 100, 41, 57, 38, 14, 52, 28, 38, 8, 46, 26, 58, 40, 60, 28, 22, 1, 82, 12, 66, 10, 94, 12, 70, 83, 72, 98, 42, 20, 94, 20, 78, 102, 105, 126, 82, 32, 66, 120, 118, 12

Offset: 1

Antti Karttunen, Apr 21 2019

nonn

Cf. A000396, A003987, A028982 (positions of odd terms), A048250, A162296, A228058, A325310, A325313, A325314.

Array[BitXor @@ Abs[#1 - Map[Total, {#3, Complement[#2, #3]}]] & @@ {#1, #2, Select[#2, SquareFreeQ]} & @@ {#, Divisors[#]} &, 88] (* Michael De Vlieger, Apr 21 2019 *)

A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A325313(n) = (A048250(n) - n);
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A325314(n) = (n - A162296(n));
A325315(n) = bitxor(abs(A325313(n)),abs(A325314(n)));

a(n) = A003987(abs(A325313(n)), abs(A325314(n))).

cp's OEIS Frontend

A325379 a(n) = A033879(A228058(n)).

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