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A087004 Numbers whose number of divisors equals the sum of their separate prime-power decompositions. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A268432 A117482 A078511 * A141055 A275819 A048541

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

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)