A322820 a(n) = A052126(n) * A006530(A052126(n)).

1, 1, 1, 4, 1, 4, 1, 8, 9, 4, 1, 8, 1, 4, 9, 16, 1, 18, 1, 8, 9, 4, 1, 16, 25, 4, 27, 8, 1, 18, 1, 32, 9, 4, 25, 36, 1, 4, 9, 16, 1, 18, 1, 8, 27, 4, 1, 32, 49, 50, 9, 8, 1, 54, 25, 16, 9, 4, 1, 36, 1, 4, 27, 64, 25, 18, 1, 8, 9, 50, 1, 72, 1, 4, 75, 8, 49, 18, 1, 32, 81, 4, 1, 36, 25, 4, 9, 16, 1, 54, 49, 8, 9, 4, 25, 64, 1, 98, 27, 100, 1, 18, 1, 16, 75

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Formula

a(n) = A052126(n) * A006530(A052126(n)).

a(n) = A122111(A000265(A122111(n))).

A052126(a(n)) = A052126(n).

a(n) <= n.

For all n > 1, A010051(n) + A319988(a(n)) = 1.

Prog

(PARI) A322820(n) = if(isprime(n), 1, if(1>=omega(n), n, my(f=factor(n), y=#f~); if(1==f[y, 2], f[y, 2] = 0; f[y-1, 2]++); factorback(f)));
(PARI)
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A052126(n) = (n/A006530(n));
A322820(n) = A052126(n)*A006530(A052126(n));
(PARI)
A000265(n) = (n>>valuation(n, 2));
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A322820(n) = A122111(A000265(A122111(n)));

Crossrefs

Cf. A000265, A006530, A052126, A070003 (positions where a(n) = n for n > 1), A122111, A319988, A322813, A322819, A322826 (restricted growth sequence transform).

Sequence in context: A368921 A322819 A089655 * A097936 A277027 A354969

Adjacent sequences: A322817 A322818 A322819 * A322821 A322822 A322823

Keyword

nonn

Author

Antti Karttunen, Dec 27 2018

Status

approved