OFFSET
1,1
COMMENTS
From Robert Israel, Nov 02 2016: (Start)
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).
It is possible that the three terms shown are just the smallest examples presently known - there may be smaller ones.
Other terms include the following (and these too may not be the next terms):
48174957112005843444270083236899591347874 = 2^7 + 1259^7 + 648383^7.
343628633008268493930426179988576850614546787655 = 5^7 + 97^7 + 6178313^7.
1556588247952374145751498792380776025975963817566087335 = 5^7 + 941^7 + 55174589^7.
6777869034345885139001456808449377853222864558972446987604 = 2^7 + 337^7 + 182635307^7.
8652931112104420195217156139788964690213217995925746635175635 = 5^7 + 29^7 + 507351601^7.
33684756195335243623428442147352712728560450053586233129585039130540009686445977 = 3^7 + 2731^7 + 229647602339^7.
4218418507660286246537768294375414778864666339784229288571328866079146694717894140 = 5^7 + 7^7 + 2677^7 + 457863123059^7.
(End)
REFERENCES
J. M. De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, page 362, ISBN 978-0-8218-4807-4.
LINKS
Jean-Marie De Koninck & Florian Luca, Partial Sums of Powers of Prime Factors, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.6 (see p. 7).
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Felix Fröhlich, Jul 26 2015
EXTENSIONS
Edited by Robert Israel, Nov 02 2016
STATUS
approved