A064623 -id:A064623 - cp's OEIS frontend

A084752 A064623(n)/s, where s = sum of the prime divisors of A064623(n).

3, 5, 7, 7, 11, 13, 13, 11, 19, 33, 19, 19, 17, 23, 23, 31, 34, 51, 31, 31, 37, 29, 37, 43, 43, 91, 95, 47, 58, 43, 47, 119, 53, 41, 143, 74, 59, 67, 67, 161, 59, 82, 73, 67, 71, 209, 71, 221, 59, 71, 89, 185, 106, 89, 221, 79, 71, 122, 83, 222, 103, 177, 103, 101, 107, 109

Offset: 0

Amarnath Murthy, Jun 16 2003

nonn

Cf. A064623.

x = vector(80); B = vector(80); i = 3; count = 0; while (count < 80, i++; if (omega(i) > 1, f = factor(i); s = sum(j = 1, matsize(f)[1], f[j, 1]); if (!(i%s), works = 1; j = 1; while (works && j <= count, if (i%x[j], j++, works = 0)); if (works, count++; x[count] = i; B[count] = i/s)))); B \\ David Wasserman, Jan 04 2005

More terms from David Wasserman, Jan 04 2005

A066031 Composite numbers n the sum of whose prime factors divides n, but which are not themselves powers of primes.

Original entry on oeis.org

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

Offset: 1

Joseph L. Pe, Dec 12 2001

nonn

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

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

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

Cf. A024619, A089352.

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

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

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

cp's OEIS Frontend

A084752 A064623(n)/s, where s = sum of the prime divisors of A064623(n).

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A066031 Composite numbers n the sum of whose prime factors divides n, but which are not themselves powers of primes.

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