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

1,1

Comments

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.

Links

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

Formula

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.

Prog

(PARI)
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), ", ")));

Crossrefs

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

Sequence in context: A331041 A317466 A045219 * A054410 A185355 A339029

Adjacent sequences: A325376 A325377 A325378 * A325380 A325381 A325382

Keyword

sign

Author

Antti Karttunen, Apr 22 2019

Status

approved