A389910 a(n) = min(n, A389909(n)).

1, 1, 3, 3, 5, 5, 7, 8, 8, 7, 11, 12, 13, 11, 12, 16, 17, 18, 19, 20, 20, 13, 23, 24, 18, 17, 16, 28, 29, 30, 31, 32, 28, 19, 30, 36, 37, 23, 39, 40, 41, 42, 43, 39, 24, 29, 47, 48, 49, 49, 51, 51, 53, 54, 42, 56, 57, 31, 59, 60, 61, 37, 40, 64, 65, 65, 67, 57, 69, 70, 71, 72, 73, 41, 36, 69, 70, 78, 79, 80, 32

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to prime indices in the factorization of n.

Formula

a(n) = a(A003961(A252463(n))) = a(2*A252463(n)).

For all n >= 1, A252463(n) = A252463(a(n)).

Prog

(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
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) };
A389909(n) = if(n%2, 2*A064989(n), A003961(n/2));
A389910(n) = min(n, A389909(n));

Crossrefs

Cf. A003961, A064989, A389909.

Cf. A252463, A323080 (rgs-transform of function b(1) = 0, b(n) = a(n) for n > 1).

Sequence in context: A245146 A339102 A095878 * A341143 A369337 A157966

Adjacent sequences: A389907 A389908 A389909 * A389911 A389912 A389913

Keyword

nonn,easy

Author

Antti Karttunen, Nov 16 2025

Status

approved