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A378231
Deficiency of prime-shifted squares: a(n) = 2*
A003961
(n^2) - sigma(
A003961
(n^2)), where
A003961
is fully multiplicative function with a(prime(i)) = prime(i+1).
6
1, 5, 19, 41, 41, 47, 109, 365, 469, 141, 155, 299, 271, 449, 683, 3281, 341, 1097, 505, 1041, 1927, 663, 811, 2567, 2001, 1211, 11719, 3509, 929, -921, 1331, 29525, 2777, 1545, 4277, 6749, 1639, 2333, 4933, 9141, 1805, 851, 2161, 5235, 16733, 3815, 2755, 22979, 13177, 6805, 6239, 9671, 3421, 27347, 6131, 31049
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OFFSET
1,2
COMMENTS
See comments in
A377879
and in
A337339
.
LINKS
Antti Karttunen,
Table of n, a(n) for n = 1..20000
Index entries for sequences computed from indices in prime factorization
.
Index entries for sequences related to sigma(n)
.
FORMULA
a(n) =
A344587
(n^2) =
A377879
(
A003961
(n)).
PROG
(PARI)
A003961
(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From
A003961
A344587
(n) = { my(u=
A003961
(n)); (u+u - sigma(u)); };
A378231
(n) =
A344587
(n^2);
CROSSREFS
Cf.
A000203
,
A003961
,
A003973
,
A033879
,
A344587
,
A377879
.
Cf. also
A337339
.
Sequence in context:
A239831
A146600
A262997
*
A031379
A125202
A024841
Adjacent sequences:
A378228
A378229
A378230
*
A378232
A378233
A378234
KEYWORD
sign
AUTHOR
Antti Karttunen
, Nov 23 2024
STATUS
approved
