|
|
A293447
|
|
Fully additive with a(p^e) = e * A000225(PrimePi(p)), where PrimePi(n) = A000720(n) and A000225(n) = (2^n)-1.
|
|
6
|
|
|
0, 1, 3, 2, 7, 4, 15, 3, 6, 8, 31, 5, 63, 16, 10, 4, 127, 7, 255, 9, 18, 32, 511, 6, 14, 64, 9, 17, 1023, 11, 2047, 5, 34, 128, 22, 8, 4095, 256, 66, 10, 8191, 19, 16383, 33, 13, 512, 32767, 7, 30, 15, 130, 65, 65535, 10, 38, 18, 258, 1024, 131071, 12, 262143, 2048, 21, 6, 70, 35, 524287, 129, 514, 23, 1048575, 9, 2097151, 4096, 17, 257, 46, 67, 4194303, 11, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Original, equal definition: totally additive with a(p^e) = e * A005187(2^(PrimePi(p)-1)), where PrimePi(n) = A000720(n).
|
|
LINKS
|
|
|
FORMULA
|
Totally additive with a(p^e) = e * A005187(2^(PrimePi(p)-1)), where PrimePi(n) = A000720(n).
Other identities:
For all n >= 2 and all k >= 0, a(n^k) = k*a(n).
|
|
PROG
|
(PARI)
A293447(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2] * A005187(2^(primepi(f[k, 1])-1))); }
(Scheme)
;; Alternatively:
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|