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A341521
Triangular array T(n,k) = A156552(A005940(1+n)*A005940(1+k)), read by rows, with n >= 0, 0 <= k <= n.
3
0, 1, 3, 2, 5, 6, 3, 7, 11, 15, 4, 9, 10, 19, 12, 5, 11, 13, 23, 21, 27, 6, 13, 14, 27, 22, 29, 30, 7, 15, 23, 31, 39, 47, 55, 63, 8, 17, 18, 35, 20, 37, 38, 71, 24, 9, 19, 21, 39, 25, 43, 45, 79, 41, 51, 10, 21, 22, 43, 26, 45, 46, 87, 42, 53, 54, 11, 23, 27, 47, 43, 55, 59, 95, 75, 87, 91, 111, 12, 25, 26, 51, 28, 53, 54, 103, 44, 57, 58, 107, 60
OFFSET
0,3
COMMENTS
A341520 is the main entry for this dyadic function. See comments there.
FORMULA
T(n,k) = A341520(n,k).
EXAMPLE
The triangle begins as:
0,
1, 3,
2, 5, 6,
3, 7, 11, 15,
4, 9, 10, 19, 12,
5, 11, 13, 23, 21, 27,
6, 13, 14, 27, 22, 29, 30,
7, 15, 23, 31, 39, 47, 55, 63,
8, 17, 18, 35, 20, 37, 38, 71, 24,
9, 19, 21, 39, 25, 43, 45, 79, 41, 51,
etc.
PROG
(PARI)
up_to = 104;
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A341520sq(n, k) = A156552(A005940(1+n)*A005940(1+k));
A341521list(up_to) = { my(v = vector(1+up_to), i=0); for(n=0, oo, for(k=0, n, i++; if(i > #v, return(v)); v[i] = A341520sq(n, k))); (v); };
v341521 = A341521list(up_to);
A341521(n) = v341521[1+n]; \\ Antti Karttunen, Feb 15 2021
CROSSREFS
The lower triangular region of A341520 read by rows.
Cf. A001477 (the left edge), A088698 (the right edge).
Sequence in context: A262395 A198755 A134237 * A227192 A360260 A099889
KEYWORD
nonn,tabl,look
AUTHOR
Antti Karttunen, Feb 15 2021
STATUS
approved