A087004 Numbers whose number of divisors equals the sum of their separate prime-power decompositions.

2, 60, 120, 180, 504, 720, 11550, 12180, 17940, 19380, 21252, 22230, 26334, 27846, 29172, 32340, 34440, 34580, 43470, 48840, 56430, 59220, 59670, 63240, 66120, 70686, 82824, 85140, 91350, 95700, 95940, 99528, 112840, 113220, 113652, 115368

Offset

1,1

References

S. Kahan, "Divisor Advisory", Journal of Recreational Mathematics 30(1) 41-4 1999-2000 Baywood NY.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)

Example

504 = 2^3*3^2*7 is in the sequence because d(504) = A000005(504) = (3+1)*(2+1)*(1+1) = 24 = 2^3 + 3^2 + 7. Similarly for 32340 = 2^2*3*5*7^2*11, where d(32340) = 2^2 + 3 + 5 + 7^2 + 11 = 72.

Mathematica

ndppdQ[n_]:=DivisorSigma[0, n]==Total[#[[1]]^#[[2]]&/@FactorInteger[n]]; Select[Range[2, 120000], ndppdQ] (* Harvey P. Dale, Nov 22 2013 *)

Prog

(PARI) isok(n) = my(f = factor(n)); numdiv(n) == sum(i=1, #f~, f[i, 1]^f[i, 2]); \\ Michel Marcus, Oct 26 2013

Crossrefs

Cf. A078511.

Sequence in context: A078511 A370881 A354770 * A328859 A141055 A275819

Adjacent sequences: A087001 A087002 A087003 * A087005 A087006 A087007

Keyword

nonn

Author

Lekraj Beedassy, Oct 13 2003

Extensions

a(1) = 2 prepended by Michel Marcus, Oct 26 2013

Status

approved