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a(n) = 0 for most n divisible by 4, except for n = 64, 96, 128, 144, 160, 192, 216, 224, 240, 256, ... These exceptions include all proper multiples of 32 but also some other multiples of 4: 9*16, 27*8, 15*16, 21*16, ...
a(n) = 0 also for some n not a multiple of 4, namely 18*(6k + 1) for all k >= 0 except 2604, 18229, 33854, ... and 27*(4k + 1) for k >= 0 different from 101, 182, 236, ..., and others.
a(n) = 48 for all numbers of the form 32*p where p is prime, and for n = 171. (Is Are there any otherothers?) This is by far the most frequent nonzero value, : it can be seen as a horizontal line in the graph of the sequence.
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a(n) = 0 also for some n not multiple of 4, namely 918*(12k 6k + 21), 9 for all k >= 0 except 2604, 18229, 33854, ... and 27*(12k 4k + 31), for k >= 0 different from 101, 182, 236, ..., and others.
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a(n) = 0 for most n divisible by 4, except for n = 64, 96, 128, 144, 160, 192, 216, 224, 240, 256, ...: these appear to These exceptions include all proper multiples of 32 but also some other multiples of 4: 9*16, 27*8, 15*16, 21*16, ...
a(n) = 0 also for some non-multiples n not multiple of 4, namely 9*(12k + 2), 9*(12k + 3), and others.
a(9*prime(n)) = 6*A067076(n-1) for n > 1. - Thomas Scheuerle, Feb 14 2024
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a(n) = 48 for all numbers of the form 32*p where p is prime, and for n = 171. (Is there any other?) This is by far the most frequent nonzero value, it can be seen as a horizontal line in the graph of the sequence.
a(n) = 11 for n = 5*709, 2*2833, 2*37*83, 2*29*107, 2*23*137, 2*17*191, 2*11*317, 2*7*569, 2*5*947, 2*3*2837, 2*3*53*67, ...: this This appears to be the second most frequent nonzero value. (End)
A356253(n) = {my(f = factor(n)); vecmax(Vec(prod(k=1, lengthvecprod(f~), [(x + f[k, 1])^f[k, 2] | f<-factor(n)~])))};
A003415(n) = if(n<=>1, 0, myvecsum([n/f[1]*f[2] | f=<-factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]), 0);
A369657(n) = (A356253(n)-A003415(n)); \\ This and above edited by _M. F. Hasler_, Feb 14 2024
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