The On-Line Encyclopedia of Integer Sequences (OEIS)

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A378981

a(n) = (A003961(n)-sigma(n)) mod (A003961(n)-2*n), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).
(history; published version)

#8 by OEIS Server at Thu Dec 12 21:55:08 EST 2024

LINKS

Antti Karttunen, <a href="/A378981/b378981_1.txt">Table of n, a(n) for n = 1..32768</a>

#7 by Michael De Vlieger at Thu Dec 12 21:55:08 EST 2024

STATUS

proposed

approved

Discussion

Thu Dec 12

21:55

OEIS Server: Installed first b-file as b378981.txt.

#6 by Antti Karttunen at Thu Dec 12 18:36:33 EST 2024

STATUS

editing

proposed

#5 by Antti Karttunen at Thu Dec 12 18:35:42 EST 2024

NAME

a(n) = A286385(n) mod A252748(n) = (A003961(n)-A000203sigma(n)) mod ((2*n)-A003961(n)-2*n), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

LINKS

Antti Karttunen, <a href="/A378981/b378981_1.txt">Table of n, a(n) for n = 1..32768</a>

#4 by Antti Karttunen at Thu Dec 12 18:34:37 EST 2024

NAME

a(n) = A286385(n) mod A252748(n) = (A003961(n)-A000203(n)) mod ((2*n)-A003961(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

#3 by Antti Karttunen at Thu Dec 12 18:18:46 EST 2024

CROSSREFS

Cf. A378980 (positions of 0's), A349753 (positions of 0's at odd n).

#2 by Antti Karttunen at Thu Dec 12 18:11:39 EST 2024

NAME

allocated for Antti Karttunen

a(n) = A286385(n) mod A252748(n).

DATA

0, 0, 0, 0, 1, 0, 0, 1, 5, 0, 1, 17, 3, 4, 1, 1, 1, 36, 3, 21, 10, 3, 5, 75, 0, 0, 14, 0, 1, 33, 5, 1, 0, 3, 1, 134, 3, 2, 1, 99, 1, 69, 3, 4, 12, 0, 5, 281, 18, 7, 2, 6, 5, 255, 0, 177, 0, 3, 1, 147, 5, 2, 22, 1, 2, 51, 3, 10, 0, 87, 1, 480, 5, 9, 26, 12, 3, 87, 3, 381, 41, 3, 5, 271, 25, 9, 16, 171, 7, 291, 0, 16, 0, 15, 12

OFFSET

1,9

LINKS

<a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.

<a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

FORMULA

a(n) = A286385(n) mod -A252748(n) = (A003961(n)-A000203(n)) mod ((2*n)-A003961(n)).

PROG

(PARI)

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A378981(n) = ((A003961(n)-sigma(n))%((2*n)-A003961(n)));

CROSSREFS

Cf. A000203, A003961, A252748, A286385.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Dec 12 2024

STATUS

approved

editing

#1 by Antti Karttunen at Thu Dec 12 18:04:04 EST 2024

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved