A391934 Irregular triangle T(n, k) = Sum_{i=1..1+n} (A003415(k) mod prime(i))*A002110(i-1), with n >= 0, and 0 <= k < A002110(n), read by rows.

0, 0, 0, 0, 0, 9, 9, 26, 9, 0, 0, 39, 39, 146, 39, 155, 39, 162, 186, 15, 39, 68, 39, 85, 52, 136, 39, 7, 39, 114, 92, 201, 39, 88, 92, 31, 193, 136, 39, 0, 0, 249, 249, 986, 249, 1205, 249, 372, 1446, 1485, 249, 1118, 249, 1975, 1732, 2236, 249, 2107, 249, 534, 2192, 621, 249, 88, 2192, 871, 1243, 2236, 249, 1989

Offset

0,6

Links

Antti Karttunen, Table of n, a(n) for n = 0..32588; rows 0-6 of the triangle

Index entries for sequences related to primorial base.

Example

Irregular triangle begins as:
n\k| 0  1    2    3    4    5     6    7    8     9    ...
---+--------------------------------------------------------
0  | 0;
1  | 0, 0;
2  | 0, 0,   9,   9,  26,   9;
3  | 0, 0,  39,  39, 146,  39,  155,  39, 162,  186, 15, 39, 68, 39, 85, 52, 136, 39, 7, 39, 114, 92, 201, 39, 88, 92, 31, 193, 136, 39;
4  | 0, 0, 249, 249, 986, 249, 1205, 249, 372, 1446, 1485, 249, 1118, 249, 1975, 1732, 2236, 249, 2107, 249, 534, 2192, 621, 249, 88, 2192, ...

Prog

(PARI)
rows_up_to = 6;
A002110(n) = prod(i=1, n, prime(i));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A143293(n) = { if(n==0, return(1)); my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); s; };
A391934_tr(n, k) = { my(x=A003415(k)); sum(i=1, 1+n, ((x % prime(i)) * A002110(i-1))); };
A391934_list(rows_up_to) = { my(v = vector(A143293(rows_up_to)-1), j=0); for(row=1, rows_up_to, for(k=0, A002110(row)-1, j++; v[j] = A391934_tr(row, k))); (v); };
v391934 = A391934_list(rows_up_to);
A391934(n) = if(!n, n, v391934[n]);

Crossrefs

Cf. A002110 (row lengths), A003415, A143293.

Cf. also A391930, A391935.

Sequence in context: A014725 A202208 A059816 * A339716 A111005 A076089

Adjacent sequences: A391931 A391932 A391933 * A391935 A391936 A391937

Keyword

nonn,tabf

Author

Antti Karttunen, Jan 05 2026

Status

approved