login
The OEIS is supported by
the many generous donors to the OEIS Foundation
.
A337337
a(n) = gcd(1+sigma(s), (s+1)/2), where s is the square of n once prime-shifted (s =
A003961
(n)^2 =
A003961
(n^2)).
8
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1
(
list
;
graph
;
refs
;
listen
;
history
;
text
;
internal format
)
OFFSET
1,14
COMMENTS
All terms are in
A007310
, because all terms of
A337336
are.
LINKS
Antti Karttunen,
Table of n, a(n) 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) = gcd((s+1)/2, 1+sigma(s)), where s =
A003961
(n)^2 =
A003961
(n^2).
a(n) = gcd(
A048673
(n^2), 1+
A003973
(n^2)).
a(n) = gcd(
A048673
(n^2),
A337194
(
A003961
(n)^2)) = gcd(
A337336
(n),
A336844
(n^2)).
a(n) =
A336697
(
A048673
(n)).
a(n) =
A337335
(n^2).
PROG
(PARI)
A003961
(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A337337
(n) = { my(s=(
A003961
(n)^2)); gcd((s+1)/2, 1+sigma(s)); };
(PARI)
A048673
(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
A336697
(n) = { my(s=((n+n-1)^2)); gcd((s+1)/2, 1+sigma(s)); };
A337337
(n) =
A336697
(
A048673
(n));
CROSSREFS
Cf.
A003961
,
A003973
,
A007310
,
A048673
,
A336697
,
A336844
,
A337194
,
A337335
,
A337336
,
A337338
,
A337339
.
Sequence in context:
A365490
A257098
A322356
*
A119788
A334561
A059592
Adjacent sequences:
A337334
A337335
A337336
*
A337338
A337339
A337340
KEYWORD
nonn
AUTHOR
Antti Karttunen
, Aug 24 2020
STATUS
approved
