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A113855 Numbers whose prime factors are raised to the powers of each other. 2
72, 800, 6272, 30375, 247808, 750141, 1384448, 37879808, 189267968, 235782657, 1313046875, 1749600000, 3502727631, 4437573632, 338751673344, 451508436992, 634465620819, 2063731785728, 7863818359375, 7971951402153, 188153927303168 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

More precisely, n is a term iff n = prod(p_i^(sopf(n)-p_i)), where n has at least two distinct prime factors p_i and sopf(n) = A008472(n). - Rick L. Shepherd, Feb 02 2006

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

72 = 8*9 = 2^3*3^2. So primes 2 and 3 are raised to the power of each other.

800 = 2^5*5^2 = 2 to the power 5 times 5 to the power 2.

PROG

(PARI) allpwrfact(n) = { local(x, a, b); a = vector(50); a[1] = 2^3*3^2; a[2] = 2^5*5^2; a[3] = 2^7*7^2; a[4] = 2^11*11^2; a[5] = 2^13*13^2; a[6] = 2^17*17^2; a[7] = 2^19*19^2; a[8] = 2^23*23^2; a[9] = 2^29*29^2; a[10]= 2^31*31^2; a[11]= 2^37*37^2; a[12]= 2^41*41^2; a[13]= 3^5*5^3; a[14]= 3^7*7^3; a[15]= 3^11*11^3; a[16]= 3^13*13^3; a[17]= 3^17*17^3; a[18]= 3^19*19^3; a[19]= 3^23*23^3; a[20]= 3^29*29^3; a[21]= 3^31*31^3; a[22]= 3^37*37^3; a[23]= 2^3*2^5*3^2*3^5*5^2*5^3; a[24]= 2^3*2^7*3^2*3^7*7^2*7^3; a[25]= 2^5*2^7*5^2*5^7*7^2*7^5; a[26]= 2^5*2^11*5^2*5^11*11^2*11^5; a[27]= 3^5*3^7*5^3*5^7*7^3*7^5; a[28]=5^7*7^5; a[29]=5^11*11^5; b= vecsort(a); for(x=1, 42, if(b[x]<>0, print1(b[x]", "))) } (Shepherd)

CROSSREFS

Cf. A082949 (numbers of the form p^q * q^p, p, q distinct primes), A008472 (sum of distinct prime factors of n).

Sequence in context: A304828 A268780 A086579 * A082949 A240983 A210627

Adjacent sequences:  A113852 A113853 A113854 * A113856 A113857 A113858

KEYWORD

nonn

AUTHOR

Cino Hilliard, Jan 25 2006

EXTENSIONS

Corrected by Rick L. Shepherd, Feb 02 2006

STATUS

approved

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Last modified July 22 16:43 EDT 2019. Contains 325225 sequences. (Running on oeis4.)