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A302755 Strongly prime-additive numbers: numbers n with at least 2 distinct prime factors that can be represented as n = Sum_{p|n} p^e_p, with e_p > 0 and p^e_p < n < p^(e_p+1). 2
228, 3115, 190233, 1090918, 11352818, 32647591, 98437335, 670402467, 809609110, 869424040, 1008317892, 8911808588, 37104085671, 243006777356, 297252832082 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first 3 terms were given in the paper by Erdős & Hegyvári. They were found by P. Massias.

Subsequence of A302753.

a(16) > 5.4*10^11. - Giovanni Resta, Aug 23 2018

LINKS

Table of n, a(n) for n=1..15.

Paul Erdős and Norbert Hegyvári, On prime-additive numbers, Studia Sci. Math. Hungar., Vol. 27, No. 1-2 (1992), pp. 207-212. Review.

EXAMPLE

228 = 2^2 * 3 * 19 = 2^7 + 3^4 + 19.

3115 = 5 * 7 * 89 = 5^4 + 7^4 + 89.

190233 = 3^2 * 23 * 919 = 3^11 + 23^3 + 919.

1090918 = 2 * 199 * 2741 = 2^20 + 199^2 + 2741.

11352818 = 2 * 41 * 138449 = 2^23 + 41 ^4 + 138449.

32647591 = 29 * 59 * 19081 = 29^5 + 59^4 + 19081.

98437335 = 3 * 5 * 6562489 = 3^16 + 5^11 + 6562489.

670402467 = 3^3 * 7^2 * 506729 = 3^18 + 7^10 + 506729.

809609110 = 2 * 5 * 211 * 257 * 1493 = 2^29 + 5^12 + 211^3 + 257^3 + 1493^2.

869424040 = 2^3 * 5 * 19 * 197 * 5807 = 2^29 + 5^12 + 19^6 + 197^3 + 5807^2.

1008317892 = 2^2 * 3 * 84026491 = 2^29 + 3^18 + 84026491.

8911808588 = 2^2 * 683 * 3262009 = 2^33 + 683^3 + 3262009.

37104085671 = 3 * 89 * 138966613 = 3^22 + 89^5 + 138966613.

243006777356 = 2^2 * 7 * 8678813477 = 2^37 + 7^13 + 8678813477.

297252832082 = 2 * 29 * 5125048829 = 2^38 + 29^7 + 5125048829.

MATHEMATICA

p[n_] := First[Transpose[FactorInteger[n]]]; powerMax[p_, n_] :=

Module[{k = 0, nn = n}, While[nn > 1, nn /= p; k++]; p^(k - 1)]; a[n_] := Module[{primes = p[n]}, np = Length[primes]; s = 0; If[np > 1, Do[s += powerMax[primes[[k]], n], {k, 1, np}]]; s]; aQ[n_] := a[n] == n; seq={}; Do[If[aQ[n], AppendTo[seq, n]], {n, 2, 100000}]; seq

CROSSREFS

Cf. A296717, A302753.

Sequence in context: A053174 A335270 A103837 * A064245 A201238 A220624

Adjacent sequences:  A302752 A302753 A302754 * A302756 A302757 A302758

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Apr 12 2018

EXTENSIONS

a(9)-a(15) from Giovanni Resta, Aug 23 2018

STATUS

approved

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Last modified January 18 17:18 EST 2022. Contains 350455 sequences. (Running on oeis4.)