OFFSET
1,2
COMMENTS
A122111 is a self-inverse permutation, so this array represents a binary operation A(.,.) over the positive integers that is isomorphic to multiplication. Its primes are the positive powers of 2 (as defined by standard multiplication): 2, 4, 8, 16, 32, ... . The positive powers of 2, as defined by A(.,.), are the prime numbers as we usually understand them: 2, 3, 5, 7, 11, ... . - Peter Munn, Aug 04 2022
LINKS
FORMULA
EXAMPLE
The top left 15 X 15 corner of the array:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
2, 3, 5, 6, 7, 10, 11, 12, 15, 14, 13, 20, 17, 22, 21,
3, 5, 7, 10, 11, 14, 13, 20, 21, 22, 17, 28, 19, 26, 33,
4, 6, 10, 9, 14, 15, 22, 18, 25, 21, 26, 30, 34, 33, 35,
5, 7, 11, 14, 13, 22, 17, 28, 33, 26, 19, 44, 23, 34, 39,
6, 10, 14, 15, 22, 21, 26, 30, 35, 33, 34, 42, 38, 39, 55,
7, 11, 13, 22, 17, 26, 19, 44, 39, 34, 23, 52, 29, 38, 51,
8, 12, 20, 18, 28, 30, 44, 27, 50, 42, 52, 45, 68, 66, 70,
9, 15, 21, 25, 33, 35, 39, 50, 49, 55, 51, 70, 57, 65, 77,
10, 14, 22, 21, 26, 33, 34, 42, 55, 39, 38, 66, 46, 51, 65,
11, 13, 17, 26, 19, 34, 23, 52, 51, 38, 29, 68, 31, 46, 57,
12, 20, 28, 30, 44, 42, 52, 45, 70, 66, 68, 63, 76, 78, 110,
13, 17, 19, 34, 23, 38, 29, 68, 57, 46, 31, 76, 37, 58, 69,
14, 22, 26, 33, 34, 39, 38, 66, 65, 51, 46, 78, 58, 57, 85,
15, 21, 33, 35, 39, 55, 51, 70, 77, 65, 57, 110, 69, 85, 91,
PROG
(PARI)
up_to = 105;
A122111(n) = if(1==n, n, my(f=factor(n), es=Vecrev(f[, 2]), is=concat(apply(primepi, Vecrev(f[, 1])), [0]), pri=0, m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A350066list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A350066sq(col, (a-(col-1))))); (v); };
v350066 = A350066list(up_to);
A350066(n) = v350066[n]; \\ Antti Karttunen, Dec 13 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Dec 13 2021
STATUS
approved