A113855 Numbers whose prime factors are raised to the powers of each other.

72, 800, 6272, 30375, 247808, 750141, 1384448, 37879808, 189267968, 235782657, 1313046875, 1749600000, 3502727631, 4437573632, 338751673344, 451508436992, 634465620819, 2063731785728, 7863818359375, 7971951402153, 188153927303168

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 A330829 A240983

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