A325819 - OEIS

A325819

a(n) = A324213(A228058(n)).

26, 84, 78, 168, 118, 146, 242, 182, 208, 276, 200, 398, 396, 322, 438, 344, 390, 412, 536, 628, 432, 338, 582, 472, 558, 840, 512, 824, 640, 726, 1022, 852, 914, 628, 744, 616, 1178, 1018, 858, 1140, 856, 760, 990, 936, 1490, 1014, 1564, 1482, 1104, 1096, 1196, 1138, 1008, 1550, 1556, 1180, 1474, 1158, 1508, 858, 2020

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OFFSET

1,1

COMMENTS

If a(n) > 2 for all n, then there are no odd perfect numbers. See also the conjectures in A324213.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..25000

FORMULA

a(n) = A324213(A228058(n)).

PROG

(PARI)

up_to = 25000;

isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));

A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(k<up_to, n++; if(isA228058(n), k++; v[k] = n)); (v); };

v228058 = A228058list(up_to);

A228058(n) = v228058[n]; \\ Antti Karttunen, May 29 2019

A324213(n) = { my(s=sigma(n)); sum(i=0, s, (1==gcd(n-i, n-(s-i)))); };

A325819(n) = A324213(A228058(n));

CROSSREFS

Cf. A228058, A324213, A325809.

Sequence in context: A260199 A239172 A291631 * A138081 A118543 A048509

Adjacent sequences: A325816 A325817 A325818 * A325820 A325821 A325822

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 29 2019

STATUS

approved