A003962 Completely multiplicative with a(prime(k)) = floor( (prime(k+1)+1)/2 ) for k-th prime prime(k).

1, 2, 3, 4, 4, 6, 6, 8, 9, 8, 7, 12, 9, 12, 12, 16, 10, 18, 12, 16, 18, 14, 15, 24, 16, 18, 27, 24, 16, 24, 19, 32, 21, 20, 24, 36, 21, 24, 27, 32, 22, 36, 24, 28, 36, 30, 27, 48, 36, 32, 30, 36, 30, 54, 28, 48, 36, 32, 31, 48, 34, 38, 54, 64, 36, 42, 36, 40, 45, 48, 37, 72, 40, 42, 48, 48

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Index to divisibility sequences.

Formula

Multiplicative with a(p^e) = ((A000040(A000720(p)+1)+1)/2)^e. - David W. Wilson, Aug 01 2001

Mathematica

f[p_, e_] := Floor[(NextPrime[p] + 1)/2]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 31 2023 *)

Prog

(PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 1] = (nextprime(f[i, 1]+1)+1)/2); factorback(f); \\ Michel Marcus, Jun 09 2014

Crossrefs

Cf. A000040, A000720, A151800.

Sequence in context: A253248 A341112 A329004 * A102443 A102441 A102440

Adjacent sequences: A003959 A003960 A003961 * A003963 A003964 A003965

Keyword

nonn,easy,mult

Author

Marc LeBrun

Extensions

Corrected and extended by David W. Wilson

Status

approved