cp's OEIS Frontend

A257659 Numbers that are not seventh powers, but can be written as the sum of the seventh powers of two or more of their prime factors.

%I A257659 #29 Nov 03 2016 18:35:03
%S A257659 275223438741,4561072096211306682,9306119954843409393442022085025276
%N A257659 Numbers that are not seventh powers, but can be written as the sum of the seventh powers of two or more of their prime factors.
%C A257659 From _Robert Israel_, Nov 02 2016: (Start)
%C A257659 Each term is the sum of the seventh powers of three or more of its prime factors (since the sum of seventh powers of two distinct primes would not be divisible by those primes).
%C A257659 It is possible that the three terms shown are just the smallest examples presently known - there may be smaller ones.
%C A257659 Other terms include the following (and these too may not be the next terms):
%C A257659 48174957112005843444270083236899591347874 = 2^7 + 1259^7 + 648383^7.
%C A257659 343628633008268493930426179988576850614546787655 = 5^7 + 97^7 + 6178313^7.
%C A257659 1556588247952374145751498792380776025975963817566087335 = 5^7 + 941^7 + 55174589^7.
%C A257659 6777869034345885139001456808449377853222864558972446987604 = 2^7 + 337^7 + 182635307^7.
%C A257659 8652931112104420195217156139788964690213217995925746635175635 = 5^7 + 29^7 + 507351601^7.
%C A257659 33684756195335243623428442147352712728560450053586233129585039130540009686445977 = 3^7 + 2731^7 + 229647602339^7.
%C A257659 4218418507660286246537768294375414778864666339784229288571328866079146694717894140 = 5^7 + 7^7 + 2677^7 + 457863123059^7.
%C A257659 (End)
%D A257659 J. M. De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, page 362, ISBN 978-0-8218-4807-4.
%H A257659 Jean-Marie De Koninck & Florian Luca, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Koninck/koninck71.html">Partial Sums of Powers of Prime Factors</a>, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.6 (see p. 7).
%e A257659 275223438741 is not a seventh power, i.e., not a term of A001015, but is equal to the product of prime numbers 3 * 23 * 43 * 92761523, and 3^7 + 23^7 + 43^7 = 275223438741, so 275223438741 is a term of the sequence.
%Y A257659 Cf. A001015, A092759.
%K A257659 nonn,more
%O A257659 1,1
%A A257659 _Felix Fröhlich_, Jul 26 2015
%E A257659 Edited by _Robert Israel_, Nov 02 2016