OFFSET
1,2
COMMENTS
Original definition, now conjectural, is "Positive integers m in increasing order determined by these rules: a(1) = 1, for n>=1, if m is in the sequence then also are numbers h such that sigma(h) = 4m-1". This is certainly equal to the new definition if 25 is the only term that is not a power of 2, as there is no x such that sigma(x) = 99 = 4*25-1. - Antti Karttunen, Dec 13 2024
If 31 is only number h of form 2^k-1 for any k>=1 such that sigma(x) = h has solution for more than one value of x then a(n) is union number 25 with A000079 (powers of 2).
Numbers k such that A000203(k) is in A000225. If Goormaghtigh conjecture is valid, then it is certain that 25 is the only odd prime power (after 1) in this sequence. - Antti Karttunen, Dec 13 2024
LINKS
EXAMPLE
These examples relate to the original definition:
m=1, 4m-1=3, sigma(h)=3 for h=2; number 2 is in sequence.
m=2, 4m-1=7, sigma(h)=7 for h=4; number 4 is in sequence.
m=4, 4m-1=15, sigma(h)=15 for h=8; number 8 is in sequence.
m=8, 4m-1=31, sigma(h)=31 for h=16 and 25; numbers 16 and 25 are in sequence.
PROG
(PARI) is_A202274(n) = ((x->!bitand(x, x+1))(sigma(n)));
for(n=1, 2^20, if(is_A202274(n^2), print1(n^2, ", ")); if(n>1 && is_A202274(2*((n-1)^2)), print1(2*((n-1)^2), ", "))); \\ Remember to sort! - Antti Karttunen, Dec 13 2024
CROSSREFS
Cf. also A202273.
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 25 2011
EXTENSIONS
Data section corrected (terms 1024, 2048 were duplicated), more terms added, and the name replaced with a new definition, with the original definition moved to the comments - Antti Karttunen, Dec 13 2024
STATUS
approved