A368988 -id:A368988 - cp's OEIS frontend

A368698 a(n) is the smallest positive k such that A005940(1+n) divides the oblong number k*(k+1).

1, 1, 2, 3, 4, 2, 8, 7, 6, 4, 5, 3, 24, 8, 26, 15, 10, 6, 6, 4, 14, 5, 9, 8, 48, 24, 24, 8, 124, 26, 80, 31, 12, 10, 11, 7, 10, 6, 27, 15, 21, 14, 14, 15, 49, 9, 54, 15, 120, 48, 48, 24, 49, 24, 99, 8, 342, 124, 125, 27, 624, 80, 242, 63, 16, 12, 12, 11, 25, 11, 44, 7, 13, 10, 44, 20, 99, 27, 27, 15, 65, 21, 21, 20

Offset: 0

Antti Karttunen, Jan 11 2024

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A002378, A005940, A344005, A368699, A368700, A368693 (rgs-transform), A368988 (positions of records), A368989 (values of records).

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344005(n) = { my(m=1); while((m*(m+1)) % n, m++); m; };
A368698(n) = A344005(A005940(1+n));

a(n) = A344005(A005940(1+n)).

For n >= 1, a(2^n) = A006093(n), a(A000225(n)) = A000225(n).

A368989 Values of records in A368698.

Original entry on oeis.org

1, 2, 3, 4, 8, 24, 26, 48, 124, 342, 624, 1330, 2400, 3124, 14640, 16806, 28560, 29281, 161050, 371292, 483153, 1771560, 4826808, 19487170, 20049821, 24318700, 62748516, 214358880, 289608539, 410338672, 815730720, 2357947690, 3234870386, 6975757440, 10604499372, 25937424600

Offset: 1

Antti Karttunen, Jan 12 2024

nonn

Terms A324201(k) - 1: 8, 124, 161050, 410338672, ..., seem to form a subsequence. See comments in A368988 and in A344005.

Cf. A324201, A344005, A368988, A368698.

a(n) = A368698(A368988(n)).

cp's OEIS Frontend

A368698 a(n) is the smallest positive k such that A005940(1+n) divides the oblong number k*(k+1).

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