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A003960 Fully multiplicative with a(p) = [ (p+1)/2 ] for prime p. 5
1, 1, 2, 1, 3, 2, 4, 1, 4, 3, 6, 2, 7, 4, 6, 1, 9, 4, 10, 3, 8, 6, 12, 2, 9, 7, 8, 4, 15, 6, 16, 1, 12, 9, 12, 4, 19, 10, 14, 3, 21, 8, 22, 6, 12, 12, 24, 2, 16, 9, 18, 7, 27, 8, 18, 4, 20, 15, 30, 6, 31, 16, 16, 1, 21, 12, 34, 9, 24, 12, 36, 4, 37, 19, 18, 10, 24, 14, 40, 3, 16, 21, 42, 8, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000

FORMULA

If n = Product p(k)^e(k) then a(n) = Product [ (p(k)+1)/2 ]^e(k).

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

a(n) = 1 iff n is a power of 2 (A000079). - Michel Marcus, Nov 16 2017

PROG

(PARI) { A003960(n) = my(f); f=factor(n/2^valuation(n, 2)); prod(i=1, matsize(f)[1], ((f[i, 1]+1)/2)^f[i, 2] ); } \\ Max Alekseyev, Jul 27 2017

CROSSREFS

Cf. A003970.

Sequence in context: A228731 A163507 A003963 * A243499 A124223 A295908

Adjacent sequences:  A003957 A003958 A003959 * A003961 A003962 A003963

KEYWORD

nonn,mult

AUTHOR

Marc LeBrun

STATUS

approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)