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A124052 Sum from 1 to n of all factors of primes less than n such that the power of any factor (p) never exceeds log(n) base p. 1
1, 3, 12, 28, 168, 168, 1344, 2880, 9360, 9360, 112320, 112320, 1572480, 1572480, 1572480, 3249792, 58496256, 58496256, 1169925120, 1169925120, 1169925120, 1169925120, 28078202880, 28078202880, 145070714880, 145070714880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) > a(n-1) implies n is either a prime or the power of a prime.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..2000

FORMULA

a(n) = a(n-1)(1+n*(P-1)/(n-1)), if n is the power of any prime (P);

a(n) = a(n-1), if n is not the power of any prime.

EXAMPLE

a(5)  = (1+2+4)*(1+3)*(1+5).

a(6)  = a(5), since 6 is not a primepower.

a(7)  = (1+2+4)*(1+3)*(1+5)*(1+7).

a(8)  = (1+2+4+8)*(1+3)*(1+5)*(1+7).

a(9)  = (1+2+4+8)*(1+3+9)*(1+5)*(1+7).

a(10) = a(9) since 10 is not a primepower.

CROSSREFS

Cf. A000203, A034699.

Sequence in context: A005995 A034503 A026557 * A215640 A104353 A001860

Adjacent sequences:  A124049 A124050 A124051 * A124053 A124054 A124055

KEYWORD

nonn

AUTHOR

Timothy Frison (frison(AT)gmail.com), Nov 03 2006

STATUS

approved

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Last modified October 17 12:33 EDT 2018. Contains 316280 sequences. (Running on oeis4.)