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A066031 Composite numbers n the sum of whose prime factors divides n, but which are not themselves powers of primes. 8
30, 60, 70, 84, 90, 105, 120, 140, 150, 168, 180, 231, 234, 240, 252, 260, 270, 280, 286, 300, 315, 336, 350, 360, 450, 456, 468, 480, 490, 504, 520, 525, 528, 532, 540, 560, 572, 588, 600, 627, 646, 672, 693, 700, 702, 720, 735, 750, 756, 805, 810, 897 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes and powers of primes have been excluded from the sequence because they trivially satisfy the condition "the sum of the prime factors of n divides n". Call a term of the sequence "primitive" if it is not a multiple of some previous term; for example, 70 is primitive while 60 is not. Are there infinitely many primitive terms? See A064623.

Intersection of A089352 and A024619. - Michel Marcus, Feb 03 2016

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Jean-Marie de Koninck, Florian Luca, Integers divisible by sums of powers of their prime factors, Journal of Number Theory, Volume 128, Issue 3, March 2008, Pages 557-563.

J. Pe, The Prime-perfect Numbers

EXAMPLE

The sum of the prime factors of 70 is 2 + 5 + 7 = 14, which divides 70.

MATHEMATICA

Select[ Range[2, 900], IntegerQ[ # / Apply[ Plus, First[ Transpose[ FactorInteger[ # ]]]]] && Mod[ #, # - EulerPhi[ # ]] != 0 & ]

PROG

(PARI) isok(n) = if (omega(n)<2, return(0)); my(f = factor(n)) ; (n % vecsum(f[, 1])) == 0; \\ Michel Marcus, Feb 03 2016

CROSSREFS

Cf. A024619, A089352.

Sequence in context: A305613 A267967 A051283 * A212666 A291046 A071140

Adjacent sequences:  A066028 A066029 A066030 * A066032 A066033 A066034

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Dec 12 2001

EXTENSIONS

More terms from Robert G. Wilson v, Dec 12 2001

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)