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A353790
a(n) =
A353749
(sigma(
A003961
(n))), where
A353749
(k) = phi(k) *
A064989
(k), and
A064989
shifts the prime factorization one step towards lower primes, while
A003961
shifts the factorization one step towards higher primes.
8
1, 2, 4, 132, 4, 16, 8, 48, 870, 16, 30, 528, 24, 32, 32, 5390, 24, 1740, 16, 528, 96, 120, 48, 384, 1224, 96, 1056, 1056, 16, 128, 306, 7920, 240, 96, 64, 114840, 120, 64, 288, 384, 140, 384, 32, 3960, 3480, 192, 144, 21560, 9180, 2448, 192, 3168, 96, 4224, 240, 768, 192, 64, 870, 4224, 416, 1224, 6960, 1191372, 192
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OFFSET
1,2
COMMENTS
See comments in
A353789
.
LINKS
Antti Karttunen,
Table of n, a(n) for n = 1..10000
Antti Karttunen,
Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to sigma(n)
FORMULA
a(n) =
A353750
(
A003961
(n)) =
A326042
(n) *
A353767
(n).
a(n) =
A000010
(
A003973
(n)) *
A064989
(
A003973
(n)).
PROG
(PARI)
A003961
(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989
(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353790
(n) = { my(s=sigma(
A003961
(n))); (eulerphi(s)*
A064989
(s)); };
CROSSREFS
Cf.
A003961
,
A003973
,
A064989
,
A326042
,
A353750
,
A353767
,
A353789
.
Cf. also
A353794
.
Sequence in context:
A012617
A012614
A018500
*
A271677
A226070
A013552
Adjacent sequences:
A353787
A353788
A353789
*
A353791
A353792
A353793
KEYWORD
nonn
AUTHOR
Antti Karttunen
, May 10 2022
STATUS
approved
